How many quests does each companion have

It looks like you've just been unlucky.

There is a group roll and the player who wins the roll says the dialogue option they chose. Everyone hears that player’s choice and the deal with the consequences of that choice.

This can lead to some interesting conversation dynamics if the leader is in the minority.

One important detail to note is that Light side and Dark side points are not awarded to the group for the choice depicted, but for each player individually according to the choice they made individually.

Source: Interview with developers

This matches what the Developers said when they walked through one of the first flashpoints - The Esseles.

Finally, the 1.1 patch notes allude that the game tries to "normalize" conversation rolls to make sure who "wins" each roll is approximately equal.

Players who spectated conversations no longer unleash an initial massive critical social roll in their next multiplayer conversation.

The above quote would seem to indicate that not getting to speak in one social roll gives a boost in your next social roll, resetting when you finally get a chance to speak.

You need to go to a private place, such as your ship or a cantina.