Oh whoops lol. Get frickin' sniped, me.

When Bill Pots copies the spell, the copy of the spell wasn't 'cast', it was copied. So the copy being pointed at a new Bill won't trigger that new Bill's ability.

Also that renders this following point moot, but I'll clarify since you're new:

When you cast Quantum Misalignment targeting Bill, she triggers to create a copy of the spell before the original spell resolves. You'll get a second copy of the spell before you get your second Bill from the original spell being cast, so there won't be a new Bill to change the target to, unless you already have two Bills at the time of casting. Like you likely will on rebound.

New Way Forward specifically has a reflexive triggered ability as part of its effect ("when damage is prevented this way ..."). It's a triggered ability that triggers off of the damage being prevented, and it goes on the stack and can be responded to.

You won that game because state based actions would have caused your opponent to lose it before the triggered ability had a chance to resolve.

Conversely, some cards like Deflecting Palm don't use this wording and don't have a trigger. If the opponent had used Deflecting Palm instead, damage to both of you would have happened at the same time and the game would have been a draw.

Yeah, you can do that.

You control both triggers, so you can order them as you like.

You don't need to choose which creature to sacrifice until you're resolving Ashnod's ability.