Yes and Yes

You must have the right defense fir the weapon your up against.

Approval (high) posts everything (mfg,research, ,,,)  Low approval hurts everything.  Note: its a sliding scale +25%.. -25% ?; not all tool tips show approval impact but it is there

defence modules as they are... almost useless, because of weapon modules lower weight, that mean that your defence will ALWAYS be lower, than enemies attak, but alsow your attak will be about 0, so your heavy armored "tank" ship will be destroyed by heavy armed analog.

Approval improvements are very good, but(!), there is no need in build many of them (1, maximum 2 per planet), and all that doing low Approval is... lowering planet pros\science\cash income and it will be so only if approval gone in yellow or red zone.

The approval boost to base production starts to be better than the improvement production bonus as the planet matures. There is no specific number because of adjacency considerations, but ballpark it's somewhere around 400% bonus where, if you cross that point, you are better off using a tile to get approval to 100%.

Instead of approval improvements you can build just more specialized improvements or farms and get great adjacency bonuses. Growth penalty is negated with adjanced food distributors and hospitals surrounded with farms. That's my point. You should just try make high approval forge world and compare its effectiveness to low approval one.

As I see defensive modules are useless in early game - you will sacrifice half of firepower to gain additional 20% HP against one type of weapon. In late game it's just a war of one-shot kills (all my military designs had attack at least twice their hull HP) so having defense will allow to survive one more salvo. In midgame I'd say it depends on specialization choices and opponent. That damn scissor-paper-shortgun (beams) is still disappointing.

A planet's total output across the wealth, research, and manufacturing categories may be computed as

[total output] = (1 + [approval modifier] + [production modifier])*([flat production bonus] + [population-based production])*
         (1 + [manufacturing fraction]*[manufacturing bonus] + [wealth fraction]*[wealth bonus] + [research fraction]*[research bonus])
         + [flat manufacturing bonus]*(1 + [manufacturing bonus]) + [flat research bonus]*(1 + [research bonus]) + [flat wealth bonus]*
         (1 + [wealth bonus]) + [tourism] - [maintenance]

Flat manufacturing bonuses are rare; the only one I can think of is Relentless in the Malevolent tree, which is supposed to only apply to the homeworld but, due to a bug in the current implementation, applies to the homeworld and first colony. Flat research bonuses are slightly less rare, being available from the Ancient faction trait and from Quantum Leap in the Benevolent tree (unlike Relentless, both of these apply to all colonies). Flat wealth bonuses, as far as I know, are only available from Promethion Pleasure Parks, whose rarity is dependent on how much Promethion you can acquire and how much of it you throw into parks. Tourism is fairly negligible in my experience, being an order of magnitude or two lower than the gross income from wealth-specialized worlds, but is useful for counteracting maintenance costs on all worlds. All flat output bonuses tend to be fairly small relative to the production-based outputs, especially on specialized worlds. Modifiers to production are relatively rare but not necessarily difficult to obtain; Economic Rings are the most common and most easily obtained, giving +10% each, and can be stacked up to 12 times (bonuses stack additively; note that getting 12 Economic Starbases to affect a single planet is not necessarily practical, and might not be optimal depending on how this affects other planets), though there are also the level bonuses on the Thalan Hives (+5% production per level) and perhaps one or two other things that I'm forgetting.

At present, the population-based production may be computed as

[population-based production] = 2 * [population]^0.7

However, according to the patch notes for v1.02, this will change to be

[population-based production] = [population]

when v1.02 is released.

The approval modifier is defined by a set of points in the GalCiv3GlobalDefs.XML file, between which the game interpolates to generate the approval modifier. Currently, these points are (approval, modifier): (1, 0.25), (0.95, .2), (0.85, 0.15), (0.7, 0.05), (0.5, 0), (0.3, -0.05), (0.15, -0.15), (0.05, -0.2), (0, -0.25); the v1.02 patch notes suggest that the points (0.6, 0) and (0.4, 0) will be added to this list (or possibly replace some of the points already on this list).

As can be seen from the formula, and with knowledge about the terms not affected by approval, it can be seen that the approval modifier can have a very significant effect upon a planet's total output, especially in the absence of other production multipliers. Going from 50% approval to 100% approval has the same effect as increasing the overall output multiplier by 25% in the absence of starbases and flat manufacturing, research, and income bonuses.

IIRC, in GC2, a defense provided 1/3 of its efficiency against other weapon types.  100 armor  would provide 33 defense against missiles.  Is that still the case?

With approval I've got some numbers.
Had a planet with 22,3 Billion People. Started with 20% Approval
and 104 Manufacture Points

@ 100 % approval 126 Manufacture Points ~ 21 % plus on Production.
Didn't care about growth as was playing with synthetic race.

Especially in the early game with unhappy population (-2 Morale) one gets
stuck with a slow economy. Because everything (Production, Income, Research, Influence, Growth) is
negatively affected. The approval affect the raw numbers before the
additional bonus.
So it won't kill you if you've got a sad population (20%) 104 vs 126 MP on some planets
but if this is the case in the whole empire its a problem.

Tipps for happy citizens

1. Patriotic trait = no large Empire penalty.
Usually each planet adds a - 0.2 Morale to each colony.
With 30 Planets you're already at a - 6 Morale.

2. Malevolent Ideology 2nd point in first raw.
Get you +1 Morale for each sucessfull invasion for the whole empire.
So with some invasions you'll never need any morale boosting buildings.

3. Technologies with add global bonus to morale like +4 ...

4. Economic starbases which add morale

5. If you really need to get some buildings for approval.