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

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.

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.

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.

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.

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.