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 play Ultra Ball if there are no cards left in my deck?
No, you cannot. Discarding the two cards is a cost not the effect, and you cannot play Trainer cards for no effect.
Source: TPCi Rules Team (2017-04-27)
What's the proper way to play a Trainer like Ultra Ball?
When playing a Trainer you first put it onto the playing field (not directly into the Discard Pile). Then you do what the card says, such as discarding two cards (those go into the Discard Pile right away), searching your Deck, showing the selected Pokemon to your opponent before putting it directly into your hand, shuffling your Deck, etc. Finally, after everything is done, put the Trainer card into the Discard Pile.
Source: TPCi Rules Team (2014-09-18)