It has been far too long since I got to play this one, but from what I an remember…
Usually an emperor can buy up to 7 legions if he starts the turn with less than 7. Some emperors can buy 1 or 2 legions more, so they can have 8 or 9 legions. They are not free and must be paid like the basic ones.Correct, except I do not recall the cost part. I have this vague recollection that the bonus legions are, in fact, bonus legions.
If there are rebel legions you can bribe them so they convert to your color. This can be done even if you have your emperor's legion limit, up to the hard limit of 10 counters.Again, I have a vague recollection that this is correct.
Then if you play with an emperor that has no legion bonus, you can keep the legions you had in that moment, even in excess of 7, but if you drop below 7 you cannot get over 7 again with that emperor, except by bribing rebel legions.This time I am pretty sure you have it correct.