If a card with eternalize is put into your graveyard during your main phase, you’ll have priority immediately afterward. You can activate its eternalize ability before any player can try to exile it.

Once you’ve activated an eternalize ability, the card is immediately exiled. Opponents can’t try to stop the ability by exiling the card.

The token created by Lazotep Archway’s eternalize ability copies exactly what was printed on the original card and nothing else, except the characteristics specifically modified by eternalize. It doesn’t copy any information about the object the card was before it was put into your graveyard. (And, as noted in the reminder text, it enters tapped!)

The token is a 4/4 black Zombie creature land with Lazotep Archway’s printed abilities. These are copiable values of the token which other effects may copy.

Playtest cards aren’t legal for play in any tournament format other than Mystery Booster Limited formats. On the other hand, we expect they will spice up a wide variety of non-tournament games (as long as everyone’s on the same page about using them!).

Playtest cards use a modified version of game symbols, such as {T} and {W}. These modified symbols should be treated as the standard symbols during play.

For many playtest cards, you’ll need to make a generous assumption that basic game rules would be updated to allow them to work. The Mystery Booster 2 Playtest Card Notes section (reproduced here in individual Gatherer rulings) provides guidance for fitting these cards into the existing rules structure.