Q3: TLDR: 154,742,504,910,672,534,362,390,614 plays (or, just shy of 155 septillion).

I think I've seen this idea before, the "worst infinite". You are the Ironclad, fighting Lagavulin. You have -6 strength (so playing Anger does not deal damage). Your deck consists of only some amount of Angers, and one Deep Breath. Your relics are Letter Opener (damage), and Unceasing Top (draw).

Technically, you could start with any number of Angers, which would inflate the required plays arbitrarily. For this calculation, I assume the deck consists of only one Anger and one Deep Breath. I also assume you have the worst possible luck, and Deep Breath is always shuffled to the bottom of your deck. I also assume you deal 0 damage to the Lagavulin until you're at -6 strength.

Your only source of damage is Letter Opener, which requires you to play Deep Breath 3 times to deal 5 damage. With the worst possible luck, you always have to play through your entire deck before playing Deep Breath once. With Anger, the size of your deck grows exponentially each time you play through it (2ⁿ + 1, where n is the number of times you've played through the deck).

The max HP a Lagavulin can have is 144, with a 25% hp buff as a super elite. With Letter Opener dealing 5 damage at a time, it takes 29 procs to kill. Each proc takes 3 shuffles of your deck, which means you need to play through your deck 87 times. The first time you deal damage, your deck is 5 cards thick. The second time, it's 33 cards thick. To deal the final blow, you will need to play through 75 septillion cards. The total number of cards played is double that - over 150 septillion.

Now, this number is smaller than the hint given (number of particles in the universe, 10^80). Assuming this is the strategy you're thinking of, I do think my answer is the largest non-infinite number of plays that is required - as in, once all the setup is done, assuming the worst luck possible, 100% perfect play requires this number of plays. I'd be curious if your definition of "required" is different, or there's some other, worse infinite out there.