Can a character who is targeted for Pulse Wave use Prob Control and force a re-roll?

All powers and Team abilities are ignored in the effect of a pulsewave.

But isn't it true that if there is a character outside the range of the pulse wave that has prob control can make the character using pulse wave reroll the attack? This is of course a totally different thing, but I just wanted to verify this.

that's correct

Could the character making the pulse wave use opportunist or perplex for the attack?

Yes, as long as the character with Opportunist or Perplex is either the character doing the pulse waving or (in the case of Perplex) a character that isn't in the range of the attack.

if an enemy figure is in range of a pulse wave attack, can that figure use a Theme team probability?

Nope, it is still the PC power, so it is ignored.