Golurk V

When using Golurk V's "Rewind Beam" attack against an evolved Pokemon, does my opponent get to put the highest Stage Evolution card into their hand if Golurk V does enough damage to KO it?

All effects of attacks must be completed before checking for KO's. So yes, the highest Stage Evolution card is put into their hand before it is KO'd.

If I attack with Golurk V's "Rewind Beam" and do enough damage to KO my opponent's evolved Pokemon that has the Vengeful Punch tool attached, does Golurk V take 4 damage counters?

No. Rewind Beam devolves the Defending Pokemon, and when its earlier stage is Knocked Out that is no longer the Pokemon that had taken damage from the attack.

Can I use Golurk V's "Rewind Beam" attack to put a Stage 2 Pokemon that was put into play via Vaporeon VMAX's "Bubble Pod" attack into my opponent's hand?

No, because while the Stage 2 is considered an "Evolution Pokemon", it is not an "evolved Pokemon" as required by the Rewind Beam attack.