It would depend if the device was removed from the btrfs pool or not, i.e., if you started the array without it, only by seeing the diags could I be sure.
Errors after the first scrub are expected, it's bringing that device up to date with the rest of the pool, as long as all errors were corrected you're fine, balance isn't really needed for this.
Yep, as long as it was never removed from the pool you just need start the array with all devices present (all should be green) and run a scrub.
Nothing special, always make sure backups are up do date, just in case.
Always better to replace than remove, but remove should work in most cases (raid5/6 still has some corner issues).
You should also reset the btrfs stats errors, take a look here, it also explains how to better monitor a pool.