How does the alignment system work

You cannot change factions in TOR — what you pick is what you get.

That said, there are small differences depending on whether you are Light Side / Dark Side, such as verbal cosmetic changes in conversation. And your choices may affect companion affection.

Flashpoints are repeatable and have up to +/- 250 points' worth of dark/light decisions among them, and Diplomacy crew missions can yield DSP/LSP as well, so you can always completely reverse your stance (although that could potentially take a /lot/ of work...).

If you do not win the conversation roll, then since you didn't say it, the companion does not get any affection points.

You have to both choose the appropriate option to gain (or lose) affection with the current companion, and win the roll.

Of course your companion must be summoned and in the group, so this only works for groups less than 4.

It is not like Light/Dark side choices where you get the points for what you chose regardless of who won the roll.