When you encounter a bane or boon, can you immediately use a Tot Flask to search your deck for the pertinent potion (ie. it's an Aquatic bane! Find that Potion of the Ocean. Or it's an Ally! Find the Potion of Glibness)?
If I encounter a bane that requires multiple checks, and immediately play a Potion of Heroism, does that prevent me from playing another item on the first check?
I believe the rule is once you start an encounter, you can only play cards that apply to the encounter itself--things that determine combat skills, or allow you to evade, and the like. For example, you can't play a Cure during a combat so you don't have to lose it as damage. You couldn't use the Tot Flask to get an item AFTER you encounter something to get what you need to win.
For the second question, I think the two checks are considered separate from each other, so each check can have one of each type of card applied to it.
You can only play a card or use a power during an encounter if it relates to the current step of the encounter. Searching through your deck for a helpful card and adding it to your hand never relates to an encounter (even if the card you are searching for does). Same with giving a card to another player (like you have two blessings and want to play a spell that lets you give one of them away--can't do that during the encounter).
Potion of Heroism relates to making a check, so can only be played during a check if inside of an encounter. If played during a check, it counts as the one item you can play on that check, so you cannot play any other items on that particular check.
Actually there has been a lot of discussions on that subject.
If I got it right, if you had a bane that would say something for example like "add +4 to your check for each potion in your hand", then you could play Tot Flask because retrieving a potion and putting in in your hand would directly affect the check. But you cannot play it if you then have to play the retrieved potion to affect the check because that would be indirect (only the use of the second card affects the check, not the use of the first one). Same as when playing a Merchant and the like.