Pyromancy 101 is exiled taught to the chosen creature as part of that spell’s resolution, just after its other effects. It goes directly from the stack to exile. It never goes to the graveyard.

You choose the creature to teach as Pyromancy 101 resolves. The teach ability doesn’t target that creature.

If you control any creatures as Pyromancy 101 resolves, you must exile it taught to one of those creatures. You can’t choose not to teach it. If you don’t control any creatures as the spell resolves, instead Pyromancy 101 is exiled but taught to nobody.

If Pyromancy 101 is countered or otherwise fails to resolve (probably because the target became illegal), none of its effects will happen, including teach. The card will go to its owner’s graveyard and won’t be exiled.

If the taught creature leaves the battlefield, Pyromancy 101 will stay exiled but won’t be taught to any other creature.

The copy of Pyromancy 101 created by the granted activated ability is created and cast from exile. You cast that copy during the resolution of the activated ability. Ignore timing restrictions based on its type.

The copy of Pyromancy 101 created by the granted activated ability can’t be taught after it resolves.

If you choose not to cast the copy or you can’t cast it (perhaps because there are no legal targets available), it will cease to exist the next time state-based actions are performed.

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.