I'm wondering if I'm on the right page to see how cohorts work.
Say we play The Elven Entanglement scenario, so, after all players have drawn their hands, one player is selected who gets Cecilla the Uprooter. That player then adds Cecilla to his hand, which means he starts with a card more than usual—both in hand and in deck—and will possibly have to discard when he resets his hand at the end of his first turn. Is this correct?
Also, what kind effects are there that can actually banish a cohort card, thus removing it from the game?
1) Correct, the people that start with cohorts start with extra cards in hand, they need to make sure they use them somehow or else they'll be discarding down to their hand size at the end of the turn.
2) Various things will do that. Scenario 0-4 has a scenario effect that can banish them and scenario 1-4 has a henchman that banishes them if undefeated. Effects that make you banish arbitrary cards can also wind up hitting Cohorts as well.