Anyways, as for what happened with Teams A and B, Anthony just used his secret move, which only activates under very specific condition... as for what it does, well... 
it increases all stats (attack and defense get a higher boost, though), heals the party, somewhat, and...
EVERYONE in the party can now hit up to five times with moves that wouldn't normally allow it, at the cost of some of the move's power, if the move is too powerful. 

As for Team D's letter, if someone opens it, they'll find a TM for either Psyshock, or Dazzling Gleam, one or the other, depending on lavul's choice.