Dominion: Het Achterland

Yes — when you buy a card you first buy it and then gain it, and “when you gain” triggers after the card is gained (the card will already be where it was put, e.g. your discard pile) (page 4).

“When you buy” only triggers on a buy; “when you gain” triggers whenever you gain the card (including after a buy or by other effects), and the player who actually gains the card is the one for whom the gain-effects apply (page 4).

No — during the Buy phase you must play all the Treasures you intend to use before you buy any cards; you may not play more Treasures after buying (page 4).

If you reveal Trader to replace the card being gained, you gain a Silver instead and the original card is not gained, so any effects that would trigger from gaining that original card do not occur; effects tied to the act of buying (not gaining) still happen (page 11).

Tunnel’s reaction only works when it is actually discarded by an effect (including discards on your own turn or another player's); it does not trigger when cards are merely put into your discard pile because they were gained, bought, or cleaned up (page 11).

Highway’s cost reduction is cumulative (multiple Highways each reduce costs by 1, to a minimum of 0), but using a card like Throne Room on a single Highway does not double the reduction because there is still only one Highway in play (page 8).