Several questions for experienced solvers, if possible:
1. When you get the new puzzle do you twist it from solved state and back in order to understand how pieces move and find proper algorithms and then scramble and solve or you scramble it immediately?
I always can't resist scrambling a new puzzle immediately, and then try to solve it without knowing how beforehand. I have been known to get stuck for a while because I never figured out any algorithms for the new puzzle yet. But that's part of the fun of discovery -- I feel like I'm actually discovering how to solve it rather than already knowing everything beforehand.
2. When exploring how pieces move from scrambled state do you need to make records in order to understand which pieces moved and which did not or you can keep all the state in memory?
When starting on an unknown puzzle, I always use commutators, which only affects a minimal number of pieces at a time. The way they move the pieces is usually quite predictable.
3. When puzzle contains many identical pieces do you use something to differentiate one from another and understand which of them exactly are moving (like pieces of plaster)?
No, I consider that cheating. I do keep in mind, though, that identical pieces mean that you may run into parity problems later on, so when I get into a situation that looks like it's a parity problem, then I know to try to swap two of the identical pieces in order to "fix" the parity.
4. How you find algorithms? Just trying several commutators learning what they do and then trying to combine with setup moves and each other in order to get the desired result?
I solved every puzzle I have using commutators only. Well, except for the big even cubes, which require one a special edge-flip algo (that I discovered on my own). Commutators are amazing... you can literally solve almost any puzzle with them, and the way they move pieces around usually follows a predictable pattern. Sometimes you can even successfully solve a particular situation just by guessing what the commutator might be.
Great thanks to those who answer.
Sorry for the late reply, I haven't been on the forum for a while.
I just like to add another note: although commutators can work for just about anything, there is another level of consideration that needs to be taken into account if you're going to solve the entire
puzzle. Commutators pretty much almost guarantee that a particular subset of the puzzle (say all edges, or all corners) are solvable. But it may not be very obvious how to solve the rest
of the puzzle without touching what you just did. For example, for the FTO (face-turning octahedron), the corners can be easily solved using commutators, but the commutators also permute the face centers in a non-trivial way. When a situation like that arises, usually the solution is to change the order you do things (e.g., don't do face centers first, since they will get messed up when you do corners; do corners first then face centers, and you avoid the problem).
So on one level, it's all just commutators; but on another level, there is also the question of what to solve first, because sometimes it matters.