x2Hand ControlYour opponent reveals his or her hand. You may choose a Supporter card you find there. If you do, your opponent plays that Supporter card. However, you make all decisions for that card. (That Supporter card is discarded.)
HypnoblastYour opponent's Active Pokémon is now Asleep.
If I use Hypno's "Hand Control" attack and I find a Supporter that searches my opponent's deck, can I choose to use it to search their deck, find a valid target in their deck, and fail that search?
Yes, you can have the opponent search their deck (within the game's time limits for a search) and you can choose for them to fail that search.
If I use Hypno's "Hand Control" attack and I find a Supporter that searches my opponent's deck, do I have to let my opponent see the deck while I'm searching through it?
Technically speaking it is the opponent who searches through the deck, but since you are the one making the choice you are allowed to see the deck contents while they are searching.