10 but two are mutually exclusive. The likely healers are Shadowheart (Cleric), Halsin (Druid) and Jaheira from BG1/2 (likely also Druid).
In addition there are 12 "mercenary"-type companions (who don't have full stories), one of each class in the game.
You can also multiclass or respec any companion freely, including out of their normal base class.
Shadowheart is generally considered one of the most interesting characters so I'm surprised you dislike her. She does claim to be evil though. Albeit in EA she doesn't do anything Evil, and disapproves of quite a few Evil actions soooooo...
Based on Early Access Bards will be more than enough.
They've changed how Short Rests work AND Bards grant an extra Short Rest per long rest.
So in BG3 you normally get 2 Short Rests per Long Rest, and each restores 50% of your HP. Hit Dice are not tracked (nor exist at all mechanically).
So with a Bard, using no spells at all, you can recover 150% of the HP of the entire party in-between Long Rests. And Long Rests are generally easy to take.
The only real use for healing spells is thus yoyoing people in combat, which any healer, including Bard, is fine for.
As noted you have 22 total people who can go with you, and you can respec any of them to any class, so BG3 has considerably more flexibility here.
Because they can potentially be influenced to be good or evil (except possibly Minsc), and the descriptions are hyping up the most dramatic thing about them, rather than focusing on their personal morals.
Breaking down initial leanings
Good:
Karlach
Wyll
Minsc
Halsin
Evil:
Shadowheart (though hmmmmm)
Lae'zel
Astarion
Minthara
Neutral:
Gale
Maybe Jaheira (but I think Good is more likely).
Either way, with the right arguments and situations (not merely "approval points" - indeed sometimes you may have to lose those to argue them round), you can apparently convince most companions to gradually better or worse people.
You're not, trust me. The Short Rest change means out-of-combat healing is less important than 5E, and with a Bard, it becomes a joke.
Hope this helps. Happy to answer other questions.