Personally, I think of Gale as a conjuration wizard, given what he says about his summoning shenanigans as a child and his friendship with the mephit who keeps his resurrection scroll.
Astarion I'd probably go Assassin, though I can see the case for Thief or Arcane Trickster (the latter given his innate magic as a high elf).
Lae'zel I could go any way. I'm leaning towards Champion just because she gives the sense of fighting being a matter of honing her own physical capability and proving her worth to Vlakith, whereas I'd usually see Battlemasters as being more studiers of strategy and fighting as part of a team (I get the sense Lae'zel wasn't much of a team-player even among her own kind!), and while EK as Siege664 says builds on her gith magic her relatively low INT in EA makes this feel a poor fit. Especially if her INT is boosted in the full release (and I think it should be!) though, I think she could work as any.
I agree on Halsin as Moon and Karlach as Wild Magic.
Minthara I know has Vengeance abilities in EA, but her story in some ways makes more sense as an Oathbreaker to me given she has repudiated Lolth (though I know that typically an Oathbreaker has turned from the "good" , rather than from one evil to another). I reckon both could work though.
