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I'm thinking about buying this for my fiancé so that we can play together, but I have one major concern: how will conversations work? Will she be capable of seeing them if I'm the lead character? Will she be able to make choices as well, or will it just be primarily controlled by player 1?

Also, how do character conversations work? As in--when a character suddenly chimes up to inform you that X and Y is happening in their own little world, will it automatically go to player 1?
This question / problem has been solved by Hickoryimage
First of all, take note that multiplayer in Baldur's Gate can be troublesome on newer versions of Windows -- I can't get BG1 multiplayer to work at all, unless I use the BG2 engine (BGT/TuTu).

Conversations take place in a Chat window.

There's some very handy multiplayer tips for BG here.