Can I choose one or more parts of Greninja V-UNION with Vaporeon VMAX's "Bubble Pod" attack, and play it on my Bench?
Bubble Pod cannot put Greninja V-UNION into play because Bubble Pod will only get one card of the V-UNION, and one piece of a Pokemon V-UNION cannot be brought into play alone.
Source: TPCi Rules Team (2021-09-30)
Can I use Heavy Ball or Level Ball to search for a Pokemon V-UNION card?
No you can't. Even if a Pokemon V-UNION has a Retreat Cost of 3 or more when it's fully assembled, you still can't search for any of the parts with Heavy Ball. And even though some of the parts don't have any HP listed, you still can't search for them with Level Ball.
Source: TPCi Rules Team (2021-09-30)
Can I use cards that search for a Pokemon, like Ultra Ball or Poke Ball, to get a Pokemon V-UNION card from my deck or discard pile?
Any effect that lets you search your deck or discard pile for "a Pokemon" will let you use that effect on a Pokemon V-UNION card; but remember, you cannot put a single Pokemon V-UNION card into play.
Source: TPCi Rules Team (2021-09-30)
Can I have less than four pieces of a Pokemon V-UNION in my deck? Or can I put multiple copies of the same piece as long as I do not exceed four total cards of the same name?
Yes you may have less than four pieces of a Pokemon V-UNION in your deck, and you can have multiple copies of the same card; although without all four pieces that will make it impossible to get it into play.
Source: TPCi Rules Team (2021-09-30)
Can I play a Pokemon V-UNION as my Active Pokemon or on my Bench during setup?
A Pokemon V-UNION is not considered a Basic Pokemon, so you can't put it out while setting up to play.
Source: TPCi Rules Team (2021-09-30)
Do Pokemon V-UNION count as one Pokemon or four for purposes of bench space or other effects?
While in play a Pokemon V-UNION is made up of four Pokemon cards, but it counts as a single Pokemon occupying only one bench space or the Active Spot.
Source: TPCi Rules Team (2021-09-30)