In some unusual cases, you may end up putting the appropriate counters on more than one permanent. For example, if you control The Ozolith when Parish-Blade Trainee dies, you'll put the appropriate number of each kind of counter onto both The Ozolith and the target creature.

Once a creature's training ability has triggered, destroying the other attacking creature or reducing its power won't stop the creature with training from getting a +1/+1 counter.

A creature's training ability triggers only when both that creature and a creature with greater power are declared as attackers. Increasing a creature's power after attackers are declared won't cause a training ability to trigger.

Parish-Blade Trainee's last ability doesn't cause you to move counters from itself to the target creature. Rather, you put the same number of each kind of counter Parish-Blade Trainee had when it died onto that creature.

Parish-Blade Trainee's last ability puts all of its counters onto the target creature, not just its +1/+1 counters.

If Parish-Blade Trainee has -1/-1 counters on it when it dies, the last ability will include those as well. This may result in the recipient also dying.