The ability will trigger again at the beginning of the cards owners next upkeep
Theme or Battle Decks do all the hard work for newbies - though that does take some of the fun out of collecting your own cards
Theres no denying Adwals abilities are useful and fun to build around, but it just doesnt make for a great Dimir commander
Your two commanders are treated individually for all other Commander rules
The first is a triggered ability: "When this permanent enters the battlefield, target player may search their library for a card named [name], reveal it, put it into their hand, then shuffle their library." (2023-06-16) Note that the target player searches their library (which may be affected by effects such as that of Stranglehold) and that the card they find is revealed, even though these words aren't included in the ability's reminder text
Ill be looking at the number of cards in your hand and your opponents hand, the amount of value gained, and the overall impact on the game