You don’t choose a target for Zoraline’s last ability at the time it triggers. Rather, a second “reflexive” ability triggers when you pay {W}{B} and 2 life this way. You choose a target for this ability as it goes on the stack. Each player may respond to this triggered ability as normal.

If a permanent with a finality counter on it would be put into a graveyard from the battlefield, exile it instead.

Finality counters don’t stop permanents from going to zones other than the graveyard from the battlefield. For example, if a permanent with a finality counter on it would be put into its owner’s hand from the battlefield, it does so normally.

Finality counters aren’t keyword counters, and a finality counter doesn’t give any abilities to the permanent it’s on. If that permanent loses its abilities and then would go to a graveyard, it will still be exiled instead.

Multiple finality counters on a single permanent are redundant.