You do suffer a production negative impact from low morale. Think of it as you aren't giving them the things they need to remain optimal. As for the overage, that's a bug.

Yep. If your Morale is 100%, you get 25% bonus to Production (which also increases everything from Research, to Manufacturing, to Wealth). If your Morale dips below 75%, you start getting a penalty instead of a bonus, and if it reaches 0%, your planets nearly stop producing things.

So yeah, Morale is important. There's just a bug in the game that causes the tooltips to not tell you how important it is.

They really do need to fix that pop limit for syntetics. On turn 6 i had 37 pop. On turn 9 I had 100% approval rateing. on turn 100 i had 7 colonies With 160 pop each. it was on normal speed standard settings With a custom civ(syntetic/prolific). it would have been even bigger if i had a bigger map.

And that was not even close to optimally played.

Listing: Population, Approval, Approval Modifier to Resistance, Actual Base Production, Expected Base Production, % Difference between Expected and Actual Base Production

1. 10, 48%, -1%, 19.8, 20.0, -1.1%
2. 10, 46%, -2%, 19.7, 20.0, -1.6%
3. 7.3, 63%, +3.2%, 18.5, 18.0, +2.5%
4. 7.3, 60%, +2.5%, 18.5, 18.0, +2.5%
5. 4.5, 97%, +22.5%, 19.2, 15.7, +22%
6. 1.9, 100%, +25%, 16.3, 13.1, +24%
7. 2.9, 91%, +17.8%, 10.8, 9.21, +17.2%
8. 3.1, 84%, +14.2%, 10.7, 9.42, +13.6%
9. 3.5, 73%, +7.2%, 10.5, 9.81, +7.1%
10. 3, 80%, +11.6%, 10.4, 9.32, +11.6%
11. 3.5, 68%, +4.4%, 10.3, 9.81, +5%
12. 4.1, 59%, +2.2%, 10.5, 10.37, +1.3%

The first 6 entries are for the homeworld, the others are for colonies. I think there's enough evidence to conclude that approval modifies base production in the same manner, or at least in a similar manner, to how it modifies a planet's resistance. This is supported in the GalCiv3GlobalDefs.XML file, which defines a set of points for an Approval to Production curve, with the curve points being a set of multipliers which range from -25% at 0% approval to +25% at 100% approval; this curve is identical to the curves defined for Approval to Growth, Approval to Resistance, and Approval to Culture.

1) Those numbers show that production is affected by approval to the same extent that resistance is affected by approval - the numbers are a little bit off but the game's rounded display numbers can account for that.  Whatever your resistance bonus (or penalty) from approval is, the same apparently applies to production.

2) I haven't tried with synthetic races, but with non-synthetic races, if you go over the cap, your population will slowly decline until it reaches the cap.

As far as I can tell, when you go over the "limit" nothing happens.

Are you saying as your moral goes from 100% to 0% there is a production penalty going from 0% to 75%?

Production goes from +25% at 100% approval down to -25% at 0.

They seem to decay by 0.1 every turn if above the max. Since the Yor can easily reach 100+ billion pop on a good sized planet by the mid game, you can generally make 6 pop a turn if you desire. That means the decay effectively eats a turn's production every 60 turns -- much, much less on a Yor manufacture specialized planet.. though the Yor is the only race I wouldn't fully specialize, since it's virtually impossible (read: a PITA) to use the thousands of manufacture you'd get in a planet per turn.

They really need to make it hurt more to go above the cap, the Yor are stupidly OP in player hands. Which is a pity, because I like them thematically and they are fun and different to play. They are a little slower to get started than the organics, but if you reach the mid-game, no one can catch them.

They don't even have to change the code -- just set the pop decay to 1 per turn and it'll be fixed.