Are Great Generals counted as Great People? (In other words, does Philosophical affect them, etc.)
No. Great General's are gotten through combat experience points, not Great People Points. It is the GPP's that are multiplied by PHI trait. GG's production rate is increased by the Imperialistic trait (+100%).
However, a settled GG will also produce +3 beakers under Representation civic, just like a regular GPerson would.

In general though, there's no point in wasting your time trying to please an AI who hates you. You're better off trying to appease the ones who already like you somewhat. As for deciding when to declare war, that decision should depend on how you feel about the state of your military compared to the state of your rival's. Ideally you should do a bit of scouting/spying before the start of a war if you're not sure what your rival's military is like. If you're confident that your invasion stack is decent enough to take out at least a few of your rival's cities, then by all means go ahead and declare war if you so desire. 

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