How does BGT handle the transition to BG2 when it comes to party members?

If I picked Edwin and killed Dynaheir would Minsc still lament about how Irenicus killed her or would he hate me? Is Minsc even there if you don't party with him?

BGT will only transfer you to BG2 within the BG2 game rules. What happens is that your character, Imoen, Jaheira, Minsc, Viconia and Edwin all get transferred with the stats they have at the end of BG1. The story, however, remains the same: Khalid still dies; Dynaheir still dies; Jaheira and Minsc are still in their respective cells, etc. It is merely a seamless continuation of the aforementioned characters within the constraints of the BG2 storyline.

So, if I killed Dynaheir in BG1, then BG2 won't recognise it and will pin this murder on Irenicus? Like Dynaheir raised from the dead and was killed a second time?

Yes. That is the BG2 storyline. It has nothing to do with BGT, and BGT does not alter that. In fact, in the BG2 storyline most of the joinable NPCs from BG1 can be found or are mentioned, resurrected or not:
Imoen
Jaheira
Minsc
Viconia
Khalid
Dynaheir
Coran
Edwin
Faldorn
Garrick
Xzar
Montaron
Quayle
Tiax

... even Hurgan Stoneblade ("Bonchy" to Nalia), Dradeel (still mad) and Shandalar (now a Lich) from TotSC. They are all there.

I wonder how hard it would be to mod in some consistency.

I'm pretty sure it would be a huge undertaking, considering the various quests involved. But really, my thoughts are that it is outside the remit of BGT to take on such a thing: BGT is not about changing storylines, but about bringing your character (and others) from one game into the next, as though it's a single game.

Why? You have to remember that BG2 is designed as a standalone game, even though it is in essence a follow-on. This is why the storyline runs as it does, so that people who have never played BG1 can still play BG2. This is nothing new in the games industry.

Well it has its limitations. Back when it was released BG2 set new standards when it came to NPC interaction. While that feature was there in a rudimentary form in BG1, it had no real impact on the game. In essence what the devs did was to establish a canon storyline starting point for BG2 so they could have that feature work the way they wanted. if theyd brought your party from BG1 with all your decissions that probably would have exceeded the possibilities of game design back then or at least would have exceeded the resources available for an IE RPG.

Yes, even if you chunked the corpse such that it cannot be raised.
In fact, when you encounter many NPCs you can tell them "hey, I killed you in BG1" and they will lampshade this.