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." 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
One of the founding fathers of Magic writing and theory was Eric Taylor, who defined it like this: "Card advantage is any process by which a player obtains effectively more cards than his opponent." If that definition seems a bit nebulous, it's because card advantage can take such a tremendous variety of forms
There is no way for the player to do anything between you naming the card and the player discarding
In total, 21 cards amongst opponents to your own seven can seem like a bad deal at first pass
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