Roger on the flat hands being bad. The piano teacher insisted from the beginning I hold my hands up and droop my arms from the elbows, which is also the posture my Mother (who taught me for the first 2 years) had learned from the typing class and her piano teacher. She learned this back when typists were expected to produce 5 carbon copies with a manual typewriter (1942).
I spent 30 minutes a day under Mother doing the Schmitt fingering exercises in the G. Schirmer book, which IMHO are designed to develop independence of the fingers. These were so boring I was allowed to read novels as I practiced, but developing muscles and neural control is not about the higher cortex, is about the hindbrain and muscles. I was assigned the piano because I had cut the pad of my third right finger off with a folding chair on my third birthday. Before piano exercises age 8 I never used the third finger without "helping" it with the fourth finger, usually pushing on the back. The Schmitt exercises worked, I can use 3 and 4 quite independently. In fact they are so independent I can use those two fingers to thread on a small machine nut, blind, behind a bulkhead, upside down, which is something no other mechanic on my shift could do.
I haven't maintained the muscles into my 62 year, having worked full time for 36 years, but am building them back up again. As far as the suggestions for fingering of editors, I have never found them very useful. My hands are quite differently shaped than those of Russians and other northern Europeans, following instead after my short limbed native American ancestors. I have a "Morton's" foot with 2nd and 3rd toes longer than the first, and my hand the 3rd finger is quite the longest. The editors seem to have a real aversion to using thumbs on black notes, which is something I do preferentially. So, IMHO, do what sounds best, but do some boring exercises to build up your 4-5 finger muscles. Schmitt really does it, Czerny not so much. Hanson I think was invented after I quit taking piano lessons (1965), I did some of those Belwin exercise books with the stick figures on playground equipment on the cover under the professional piano teacher, but those didn't build muscles nearly as much as Schmitt exercises did under my Mother.