1. Does it matter if thf gets last hit?
2. Does it matter if thf has any form of hate on the mob with the desired drops?
3. Does the range of the thf from the mob have effect?
4. Does it matter if the thf is in the party who gets the kill shot?
5. Does it matter if the thf is in the alliance who gets the kill shot? (Multiple alliances in dynamis)
1) No, this was definitely dispelled by a SE interview at some point, who gets last hit is totally irrelevent.
2) In my experience from my year and a quarter or so of leading Dynamis, yes. Matters a hell of a lot. Whenever we have a THF pull in Dynamis our 100 Piece drop rate goes way up as opposed to having a NIN or someone else do it. The THF has to have hate to the mob in question in order for the TH to apply, just having them in the party will not do it.
3) I see no reason to believe this would be the case. Though being out of hate range might have an effect.
4) Possibly. A lot of people have observed better drop rates when the THF is in the BLM party in Dynamis, but I honestly think that it's just placebo because a THF In the BLM party is more likely to tag the statues with TH than one who is elsewhere. My personal opinion: No.
5) I'm not sure if it matters one way or another, but if I were you I'd put a THF in every alliance in Dynamis if you possibly can just to be safe, I mean, why not. 18 slots, it might be supersticious, but it's a nice precaution incase it is true.