If Scolding Administrator has -1/-1 counters on it when it dies, that ability will include those as well. This may result in the recipient of the counters dying.

Scolding Administrator's last ability doesn't cause you to move counters from Scolding Administrator onto the target creature. Rather, you put the same number of each kind of counter Scolding Administrator had when it died onto the target creature.

If enough -1/-1 counters are put on Scolding Administrator at the same time to make its toughness 0 or less, its last ability will see all of the +1/+1 counters it had when it died as well as the -1/-1 counters it had, and an equal number of each of those types of counters (plus any other applicable counters) will be put onto the target creature.

A repartee ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack.

In some unusual cases, you may end up putting the appropriate counters on more than one permanent. For example, if you control The Ozolith (a card from the Ikoria: Lair of Behemoths set) when Scolding Administrator dies, you'll put the appropriate number of each kind of counter onto both The Ozolith and the target creature.

It doesn't matter if the creature or creatures targeted by the spell that caused the repartee ability to trigger leave the battlefield or stop being creatures before that spell resolves. As long as that spell targeted one or more creatures when it was cast, the repartee ability will trigger and later resolve.

Scolding Administrator's last ability puts all counters that were on Scolding Administrator onto the target creature, not just its +1/+1 counters.