Civilization – Do Great General’s effects stack in civ 5

Yes, it does stack. I played a game where I had multiple knights which were all leveled up with both March (heal every turn) and Medic (+1 heal to unit and adjacent). When they ended the turn surrounding each other, they'd be able to get more than +2 (depending on how many Medic units were next to them).

If happiness falls below -10, you get a -33% combat modifier.

If you do not have enough strategic resources (less resources than units that require that resource), all units that need the resource get a -50% combat modifier.

I assume the combat modifiers from social policies apply also to you, if the AI civs have the appropriate social policies, but I never saw that in action. Most of these are also not strictly global, but depend partly on enemy/friendly territory or nearby units. The Total War social policy is global, if the AI researches it it should count against you.