You can't use two items on the same check, so you can't use the boots to pull thieves tools and then use the tools.
If you are allowed to immediately explore again, you can not cast augury in between.
Note: These answers are for the standard rules (aka home game), organized play has different rules for replaying scenarios.
1. When playing a scenario, the cards in the box should not have numbers higher than the number on the scenario card. So if you're replaying a 2 scenario, there should not be any 3+ cards in the location decks or the box. Since unmixing the cards is time-consuming and annoying, the easiest way to handle this is to replace the card with a random card of the same type if the one you got was too high.
Note this restriction is only on cards in the box, feel free to have higher cards in your character deck. That said, you may not want to replay scenarios that are far too under your character's "level" (aka the highest numbered card in their deck), as they'll be trivial.
2. During an encounter, you can only play cards that directly relate to the encounter. So, for A: No, your girlfriend cannot use the boots to get back a thieves tools (and even if she could, she can only play 1 item on any given check). For B: Depends on the wording. Most cards of that ilk say "immediately explore again" which means the exploring has to be the next thing you do -- playing cards or using powers in between is not allowed. If it didn't say immediately, then yes you could play Augury.
1. I'd suggest not doing it if you have cards "above" the adventure deck number of the scenario you're trying to farm; but nothing in particular is stopping you from that in general play. As for seeding the location decks, the "if the encountered card is invalid, replace it with a valid card" solution is best.
2. Both are disallowed.
A is disallowed because "retrieve a certain card from your discard pile" is not related to any step of an explore, and Footpad's Boots don't have a specific exception.
B is disallowed because if you get explores during an encounter, you have to use it the first moment it's possible (or "immediately" in game terms.)
So the sequence is this.
-Check to defeat barrier
-Succeed at check
-Clean up encounter, banish the barrier, gain the explore
*End of encounter*
-Use the explore or lose it
If you cast Augury (or Cure or anything else,) you are not taking the explore immediately, so you lose it; if you want an explore after the Augury, you'll have to pay for it in the usual ways.
Chief Technical Officer
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I'll just point out that, unless you're playing in the Adventure Card Guild, there is technically no voluntary replay of scenarios that you already succeeded at in the game. The Adventure Path tells you to complete adventures in a particular order, and the adventures tell you to complete scenarios in a particular order. The only place the rulebook addresses replay is on failing to complete a scenario.
If you want to allow replay by house rule, I would strongly suggest that you take both box composition and deck composition into account, or you could easily make your life way too easy—or way too hard. You might consider basing your house rule on the replay rules in the Adventure Card Guild, and only replay scenarios within one adventure deck number of the highest adventure deck number in your deck (which is to say, if the card with the highest adventure deck number in your deck is from adventure deck 4, don't replay anything from Adventure 2 or lower).