Dominion: Alchymie

Yes — a card that lists [Potion]+X requires a Potion plus the listed coins to buy, and you must spend one Potion for each card you buy that has Potion in its cost (you can't buy two Potion-cost cards with only one Potion). (Rulebook p.3–4)

No — phrases like “up to N” only include Potion if the specified cost explicitly includes Potion; a card costing Potion+1 is not considered “costing up to 5” in coin terms. (Rulebook p.4)

No — University cannot gain cards that have Potion in their cost; it only gains Action cards that cost up to the listed coin amount and do not include Potion. (Rulebook p.10)

When played, Philosopher's Stone produces coins equal to floor((your deck + discard pile size) ÷ 5) counted at the moment you play it; you must play Treasures (including Philosopher's Stone) before buying, so you cannot play it after you have already bought a card. (Rulebook p.8; see Treasure-play timing on p.5)

The possessed player is taking the turn (you simply make their decisions), and any cards trashed during that Possession turn are set aside and then returned to the possessed player's discard pile at the end of the turn (they still count as having been trashed for relevant effects). (Rulebook p.8–9)