At... lets say Professional REL, can you declare you are going to cast Fireball for 3 targeting your opponent's face, and then decide to take it back before you tap your mana for it (You have 4 untapped mountains)?

if this is in relation to the thing in YMtC, I'm not sure the answer applies because there can be no strategic benefit in doing so here. maybe you could draw some parallels in a case where you declare it and, before choosing targets, your opponent shows you a counterspell from their hand, introducing new information, but then that's still different because it's non-mechanical information and one could argue that your opponent had a reasonable expectation that you were going to finish casting the spell you'd announced.

Well, that is actually on your opponent for out-of-order sequencing (I think, I vaguely remember similar scenarios being described to explain... something, maybe backing up the game?). Regardless, even if it isn't a one-to-one correspondence, I figure the answer and reasoning behind it will be at least tangentially useful.

Generally, if you immediately decide not to do something after all, with little to no hesitation, you're going to be fine to back it up, no matter what REL you're playing in.

It's when you hesitate that problems may arise, because if you've had a chance to gain information about your opponent's responses (or lack thereof), a judge may be asking you pointed questions about why you changed your mind. Fishing is for the lake (or possibly the ocean), not a Magic tournament.

You should just ask zammm about the YMtC scenario DD.

YMtC scenario...?

Fairly certain these are what spurred this question.

Free first-turn Mox/Black Lotus/Academy/Workshop/Chalice of the Void tutor? Seems good.

Yeah, having the opponent set the cost and then trusting the player to pay that cost really doesn't work at all, because you can't force the player to produce the necessary mana. You'd immediately run into the kind of "But if I have Suppression Field and Goblin Test Pilot, I can just keep trying and refuse to pay until the random target's what I want to hit!" shenanigans that would get players who tried it into trouble in competitive play, only this is just one card with no setup required.