1) Yes, there is: if I recall correctly (sometimes it's hard to remember what applies to DA, DL and TA if the 3 versions act differently) 100% approval means double the population growth on that particular planet.
Super breeder means that with 100% approval you get 8 times the population growth on that particular planet.
This helps a lot in getting your population up fast, important both for colonizing and for getting your economy in the green sooner.

2) There is no "best answer". Personally I often turn them into cash machines; I prefer better quality planets for production and research, thus optimizing the bonuses I get from research coordination centers and the likes, while plenty of low quality planets full of economic buildings still provide a nice income.
It's often best not to colonize them too early if you already have the better quality planets in that star system under your control. Let the AI have them at first and get through the difficult years where population is not high enough to be profitable; at some point your influence should be enough to flip those low PQ planets to your control.

I recommend changing the bonuses you pick as soon as you feel comfortable with your regular approach; different bonuses will motivate you to try out different playing styles. That being said, I very often go for economic, research and creativity bonuses myself.

Just wanted to quickly reply on that; on your homeworld you typically build your political capital (and with some luck you have an approval bonus tile), which helps greatly to keep morale up during the early game. But it's true it's often more profitable to have your other planets at 100% and your homeworld at anything above 76%.

Most of the life on this forum has shifted towards the metaverse empires; you'll hopefully notice there are still plenty of expert players around that are willing to help and offer advice.

Heheh, in fact it's close to 3 years now since the first Gal Civ II release

I'm not sure whether the old Ctrl+N bug still exists, but previously (DA/DL) too many times trying Ctrl+N would bring the AI down to its lowest difficulty level. Unfortunately the search function doesn't work well on this forum, but there has been plenty of discussion around that topic so the answer is out there somewhere.

I would recommend never to ignore an approval tile on your homeworld. Once the population reaches its maximum, you need at least a good approval building (e.g. political capital) to keep approval reasonably high, even better if it's on an approval bonus tile.

If my homeworld has great production bonus tiles, I sometimes make it a mix of manufacturing capital, econ capital, political capital, a handful of factories and a few econ buildings. Usually though it's one of my other planets that has a 100% or 300% manufacturing bonus, so I build my manufacturing capital there.

I've moved from challenging to crippling difficulty in the past few months. I would agree that it's tough to keep up with the AI if you take a long time to get your economy up at higher difficulties. Up to normal difficulty it doesn't matter much, but even at challenging I've managed to lose from some AI races because I could not keep up in terms of economy. The huge boost from your econ capital early on makes a tremendous difference. Waiting until you capture AI capitals before building your econ capital would be quite a waste in my opinion.

The most in-depth source I know of, except for some of the experts on this forum who will hopefully chime in, is the wiki:

https://www.galciv.wikia.com/wiki/Population

It doesn't seem to include any changes introduced by Twilight of the Arnor, but plenty of the formulas will still be the same when it comes to population growth.

I build usually a starport on small planets, a factory/research building (depending if I go all-lab/all-fac) and if some space is left then this is a good place for a wonder.... maybe those that the AI usually doesn´t research, so the small planets has alot to do until all tiles are outbuilt.

Concerning the Econ-buildings: their benefit is applied on a %-rate, meaning, the higher the pop is the more $ will flow from one building; therefore their most efficient use is on worlds that are able to support a high population; eg. through moral tiles, moons, or first colony etc.... Small PQ 3+4 might not even raise 6mil inhabitants - allthough you can fly them in, and it is hard on small planets to keep moral high, I think there is an approval-boost applied when going beyond PQ +10 etc. But I´ve seen PQ +4 planets going to PQ +13 after researching Soil techs, so not all small planets might be that bad later on...

I think there is no static answer. Of course a planet´s output that has a Tech Cap will be mostly great when only Tech building are applied, (same goes for Manu Cap etc) but question is whether you have the economy input that is even able to support this output? And if not, Econ buildings might as well help on these planets, too....

Concerning manufacturing, try to match the output of each planet with the excact bc a ship will cost (or a division of that...) because any excess manufacturing is lost.... so its much better to overbuilt an Manu building with a Stock market, that way your Manu output will most likely be the same, but your $ income has increased....

Concerning Pol Cap - you can use it to sway moral in nearby worlds, and/or increase you influental range on sectors bordering alien races - this will boost your Tourism-income then; esp. on small maps to is a good factor in income.

As for the population growth/ approval-rate thing, well, I do it like this: keep it to 45% from the start; once the colony rush on my side is over change to 100% - as long as I can support this; then go back to 45% until all planets have maxed out population; and then going as low as you can, sometimes even below 30% - always keeping an eye on the Next Election-info, to raise the slider one day before to above 50%.

And for the starting-game bonuses, I have to say that Creativity can be helpful and Luck is very important if you are going to play a warfighting game. Luck determies from what point-on your dice roles, e.g. having Luck + Universalists will give half the defense etc even in the worst case. Hitpoints + Repair is pretty good if you are going to built big capital ships and try to keep them in order to be upgraded. Some ships I had had HP+400 and more, they are really worth the upgrade to better weapons systems then... Though most important in economics, without money you can´t do anything; although I'd like to know how these bonuses on Manu/Tech are applied: (1) Do they simply lower the cost needed for researching a Tech (or lower the cost a ship has) ?, (2) or do they act as a multiplier to actual pruduction? Because then, an actual bonus in these two fields is worthless if your econ is too weak to support is... or the other way round... if you have such a good economy that money is left then there is still the option to raise production by adding some planetary structures... So seen from that perspective Economy is most important, although if (1) is correct then there´s no difference.... Would be really interesting to find out, because that +20/+20 bonuses from the Mercantiles is heavy; +20 Research +1 Sensor is even heavier in terms of distribution points....

1)  About the population growth/100% approval, it depends on a lot of things and there is no general answer.  I will say, though, that at all times having 100% approval for planets below 2.5B population is CRITICAL.  Above that number, population grows linearly, meaning 100% approval will double that growth.  But below that number, population is growing exponentially.  Believe me, you want to double your exponential growth!  Your homeworld tends to be well above that 2.5B number, so 100% approval is only nice to have for it.

The earlier in the game, the fewer economic bonuses you have, so you might as well focus on growing your population now, and then later you can milk them for money when you can add more bonuses to it.

2)  About the low-PQ planets, first I will say they are valuable.  Because there's that cap on population growth rate, it's important to have lots of planets, because each planet is growing.  In other words, if you have 4 PQ 7 planets at 2.5B population, you will be gaining 4X the population growth than a single PQ26 planet with 10B on it.  Plus throw in the morale and farm issues, and that your tax is based on the square root of your population.  You want those planets.

The exception might be those REALLY low PQ planets, like PQ1-5.  Those can really drag down your economy early on.  Nifty thing you can do:  you can trade/gift them to your "friends", and let it drag down THEIR economy instead.  What's going to happen?  They're probably going to influence flip back to you anyway.  This is after your friend has invested all kinds of bc's into improvements and maintenance, and their population growth that whole time now becomes YOUR population growth.

The PQ6-8's I tend to keep, but I tend to ignore.  If my economy's not doing too good, I'll set them to not build anything (except maybe develop any bonus tiles);  just let them sit there and contribute a little to my research and grow their population.  As the budget gets more balanced, I'll gradually start turning these planets on and start building things--usually cheap stuff, like transports, constructors, scouts, defenders.  Sometimes I will also build certain unimportant wonders on them, if I'm confident the AI will probably not beat me to it.  Or if my budget's really green, I'll just buy really important wonders outright; and if that's the case, these low-PQ's are the planets those belong on.

Another trick I will do:  build really expensive warships on these planets in peacetime.  But that's going to take a really long time, right?  Yep, you got it. But you pay maintenance on warships.  If it's peacetime, why pay maintenance on expensive warships if you don't have to?  You don't pay maintenance if the ship is still building.  Just keep adding more and more credits over time; keep researching more and more powerful ships over time.  The more you research, the more expensive the ships get.  And then if there's ever a surprise war, you're always 1 turn away from an emergency ship.  Bingo--that PQ7 just actually did something useful!

I actually design these absurd ships for this purpose--like I'll pile on nothing but a bunch of survey modules onto a cargo hull.  Useless, ridiculously expensive, but I never have any intention to actually complete building one.  I just let my PQ6 take forever building my 345bc "survey" ship until later on, when I actually am able to build real ships that really do cost 345bc.  Then I just switch my starport's production to the new ship when I need it.

Yes, you can strip a planet of population. But the AI won't pay much for it.

Instead, put a bunch of transports in orbit - enough to depopulate the planet. Then sell the planet without launching the transports - the AI will pay for a fully populated transport, but since all ships in orbit launch when ownership changes hands, you get several filled transports and they get a unprofitable planet.

That trick with putting transports in orbit is sneaky, but a bit late in the game for me.  I may use that trick in ToA on extreme colonization planets.  If you invade a red planet while it's still red to you, you probably have the transports lying around anyway. 

Anyway, the point is to give your "friends" some white elephant gifts.  If you happen to get something out of a trade, that's just a bonus.  They're vulnerable to a drag on their economy at the same time you are:  during the colony rush.