If You are not playing a bard or paladin, then does it have any effect on the gameplay, or story, if You have a charisma 10 (or lower), or it effects dialogues and other things, like in PlaneScape Torment?

In BG1 a low charisma can lead to NPC's reacting badly towards you, e.g. not wanting to join your party.
In both games it has a influence on prices and on some dialogues and rewards. (not gamebreaking)

In BG1 charisma has quite an effect on NPC behavior, just like in real life. Just play the prologue with 18 charisma and then replay it with 17 charisma and you'll almost cry when you realize how badly you're treated in comparison for doing the same.
The difference will be quite big in the prologue and the FAI but later in the game it won't matter that much any more.

With 18 cha and no reputation modifier or 16+ cha and 13+ reputation or ... you'll always get the best reactions, so you can just put Imoen at position 1, get your reputation up and have her do the talking if you have low cha and still want the best reactions.

In BG 1, charisma is useful for interactions with NPC and trade. There are some NPCs (including Imoen you get very early on) who have good charisma, and you can temporarily put them as leader, so you don't need high cha on your PC.

In BG 2, you get a ring that sets charisma to 18 very early on. So it's pretty much a dump stat in that game.