Morale and Approval, what is the difference?

Loyalty helps against influence, Morale/Approval/Happiness does squat. To boost loyalty, other than with Race Abilities and anomaly bonuses, you can build Re-education Centers to prevent defections. IIRC. I never had to do it myself, mostly it's me who's conquering.

I see squares on my planet that have +100% MORALE bonuses. I have buildings that affect my APPROVAL. Are these 2 the same thing?

Yes.

Morale affects population growth/loss and election outcomes. The only effect it has relating to influence is that planets with very low morale will more easily defect once an opponent's influence has covered that planet sufficiently.

Is there any way to lower an enemy's morale on a planet? I had a major enemy planet way in my territory. His influence was at about 13 (so he was triple the minimum to flip to me) with the pirate icon. I never bothered to conquer it because I expected it to flip any turn and the large population would have been a pain to invade. That planet lasted more than two years, and only reverted to me when the civ surrendered.

It would be cool to be able to lower the morale of a planet, both to encourage it to flip and to make information warfare easier.

Put several loaded up influence bases around the planet. The effects stack.

Not in GC2, but in DA you will be ably to sabotage morale buildings, etc, via spies.