If Bramblewood Paragon enters at the same time as another Warrior (due to Living End, for example), that creature doesn't get a +1/+1 counter.

The effects from more than one Bramblewood Paragon are cumulative. That is, if you have more than one Bramblewood Paragon on the battlefield, Warrior creatures you control enter with that many additional +1/+1 counters on them.

If a Warrior would normally enter with a certain number of +1/+1 counters on it, it enters with that many +1/+1 counters plus one on it instead. If a Warrior would normally enter with no +1/+1 counters on it, it enters with one +1/+1 counter on it instead.

The creature gets the counter if it would enter under your control. It doesn't matter who owns the creature or what zone it enters from (such as your opponent's graveyard, for example).