You can undo multiple moves during the pre-fight puzzle phase as long as you don't confirm the final move. Usually the more elaborate 3 move puzzles make more sense if you take a few experimental moves then reset back to the starting position after.
You can get the healing or hint bonuses from the toad cheers with only around 200 coins most of the time, only cap it out to 999 if you really need it or can afford to splurge.
Some of the toads you rescue out in the world require backtracking from later areas, so don't get gung-ho on trying to 100% them on the first pass. There's at least 1 that won't show on the toad detectors at all and requires a missable optional item from a later area to show up.
There's an audio cue when the pre-fight puzzle timer runs low and you can refill it as many times as you want, so don't sweat checking it while figuring out the slide puzzle. It may even be a good idea to screen shot the controls during the phase to check them since it took me an embarrassing amount of time to realize clicking the R stick puts the view vertically.
The game's not Thousand Year Door and very much isn't trying to be. The world exploration and puzzle-based battling isn't for everyone, but the design does make an internal sense, so try to take it at face value. I see a lot of TTYD comparisons online and they seem to drag down enjoying the game for not following conventions that don't match the type of game this actually is.
Battles get you confetti and coins, and not much else. If the battle system is grating on you, avoiding them won't impact the game. Any battle required by the plot will be unavoidable. That being said, battles are one of the easier ways to get coins and confetti if you're running low.
When in a battle, you can open Olivia's Hint box (default button is X) and effectively stop the timer while you study the board. You won't be able to make experimental moves, but if you just wanna look at the board for awhile without losing time, this is the best way to do so.
The game has a pseudo-dynamic difficulty setting. Certain puzzles or challenges will become easier (sometimes for a price) if you fail more than a couple times in a row. The battles do get harder as the game goes on, so you probably want to at least do enough battles as you go that you get a good grasp of how the puzzling works so you're not dumped into the deep end when the difficulty increases.
You will unlock a Toad at Shogun Studios who (after finding him) will give you free hints to any Max HP hearts you've missed. He is very hard to miss, but found next to the warp pipe for that area.
There are several tools found later in the game that help make 100% completion easier.