How to figure out what is "correct" fingering and what is not? I asked some pianists that question and I've got 3 versions of answers from each of them followed by advice to try out and see what works for you. So what is "correct" fingering then?
A lot of the fingering remarks at this stage were about legato. In the easy Beethoven Sonatina in G, you have sort of a reversal of my earlier story - the downward movement is in the top notes here. There's a sequence of two chords, D-A and D-G in bar three. You could easily do both of those 51-51, but then the possibility of joining the two upper notes would be lost. The "correct" fingering would be 51-52, lifting the pinky and doing a nice legato on the top notes, one that follows into bar 4 with 53. It makes a world of difference when you hear how it sounds with a proper chord legato applied.
If you don't have a teacher, the next best thing would be to make sure you have a good edition with the proper fingerings added. Something like Alfred Masterwork, or the newer Schirmer Performance - both are relatively inexpensive and nicely edited. But then you will get just the fingering without the reasoning behind it.
At least in some cases, yes. For me, that's the real point of having a teacher - learning the thought process, not the pieces.
One thing worth mentioning is that sometimes the correct fingering for a piece is contextualized. There are pieces that you might treat as a goal in their own right, but they might also be just a stepping stone to other pieces. For example, you might see a sequence of three notes in the left hand, and there will be a "correct" fingering that's most comfortable for just those three notes. But the teacher that suggested this piece knows that those three notes can be seen as a simplified version of a six note pattern that occurs throughout a more difficult piece you will tackle later. So the "correct" fingering they suggest to you is the fingering that's most comfortable for the more difficult version you haven't played yet. You're not looking at the piece as-is, you're thinking of it in the context of what you'll eventually play and optimizing the fingering for performance of the target piece.
You will often hear that "correct" fingering is the one most comfortable. This is only partially true when you're in the early stages. Often, you go for something that's suboptimal in a particular piece because it will be more comfortable in another piece down the road.
Can you point out to such "agreed" fingering somewhere? Because as a self learner I perhaps had no chance to know which one is it?
For the chromatic scale, I was taught to alternate 3 and 1, using 2 when there are two white keys in a row.
It's a bad idea to finger on the first play or the first day because there's a risk of premature optimisation. It doesn't take much analysis apart from one or two specific problems. The fingerings I end up with usually vary somewhat from the editor's.
But the OP is correct, once you've got a fingering, you have to stick to it, even if it's suboptimal in places. It's your fingering, and if you change something after 200 repetitions there's a danger of slipping back into the old pattern and stumbling.
People have different sized hands, and different hand strengths, so some fingerings may be more damaging to a pianist's hands, and some might be more comfortable but break down at higher speeds, and some might simply be impractical at any speed.