0. Perhaps everyone knows this, but I'll just say it in case it wasn't clear: these are both cards that you want to pick up early. If you're buying your potion on turn 8 or 9 for a scrying pool or apothecary, you're going to lose (contrast golem and possession).
1/2. Apothecary counters jester very well, although nothing hurts more than a stolen alchemy card when the opponent didn't buy a potion. In theory, it counters mountebank for the same reason, but in practice the early potion investment likely prevents you from buying an early mountebank, so it's not worth it (for this reason, I might consider going for familiar over mountebank on a board with apothecary, although I've never thought about it).
1. apothecary is an A+ counter to ambassador. open ambassador/potion, get rid of one estate instead of two coppers; win. (n.b. i lost to amb/amb doing this yesterday! but i didn't get my ambassador till turn 5, so i blame fate instead of myself, which is actually the best strategy for getting better at dominion.)
2. scrying pool loves a mid to late game saboteur if there's extra actions around. scrying pool's spy ability can guarantee the saboteur will hurt, and saboteur makes up for scrying pool's slowness by effectively buying you a duchy that doesn't crowd up your deck each time you play it.
3. i'm going to disagree that potion opening is mandatory for scrying pool. scrying pool wants some trashing, so a moneylender or remake is sometimes a better opening (but definitely get a potion before you shuffle again). if there's pawn or especially hamlet on the board, i might even open remodel! still, usually potion.
4. one other possible scenario for delaying the scrying pool purchase a shuffle is university. Sometimes it's a horrible trap, but if there's, say, market or highway, it might be worth losing the pool split 6-4 to have a much more action-dense deck.