Is there any game-mechanic difference between hostile and friendly takeovers?
At this point, no. There should be, in the future. As we've stated since 2012.
Do Friendly takeovers make the population like you more?
No, but it should. See above.
Do Brutal takeovers complete faster?
No (I think).
Is there a point to balanced TO options?
Being a maverick? I think there may be (either implemented or planned), but not sure on what they may be.
If your unit has more men, how much more effective are you at TO actions by contributing percentage?
You should know by now we don't give out those specific details. Suffice to say, the more men you have, the more effective you are at supporting takeovers.
When TO's are complete, shouldn't the region be at core control initially before depreciating?
I don't think it should, but am not 100% certain on post-TO region statuses.