Okay but even as a native hungarian i have to say “sz” is just insane. Polish is so much more logical with “s” making the non-shushing sound and “sz” making the shushing sound.

Totally agreed. Like, also, everything else that you mentioned, but especially this. I really don't get where they got the idea from, since every (most?) language around has it the other way around, including Latin and German (and their derivatives like romance languages and such). Maybe Turkish and/or Romanian that I can think of, but AFAIK even they put diacritics on their 's' when referring to the 'sh' sound (I don't speak any of those, though, so I might be horribly wrong).
It's especially annoying because most Western European speakers are more used to the Polish sz-s system (which makes more sense), completely butchering words like Szoboszlai (I'm playing E-Football and the commentator pronounces his name like three different wrong ways, about never right).

I had a relatively old teacher ~30 years ago that said 'j' and 'ly' are pronounced slightly differently, giving two examples, and I couldn't hear any difference : ).

I used to go to uni in Szeged so it was quite eye-opening reading about the weird 'e's. So if I got that right, that's the reason they say stuff with 'ö' instead of 'e' in certain cases (because it's not exactly 'ö', but that's the closest regular letter we've got)?

And yeah, 'bicikli' is actually pronounced more like 'bicigli' (or not? Could be regional) and stuff, but what I meant by 'consistent' is that almost always if you see something spelled a certain way you can expect it to sound that certain way, without bullshit silent letters and completely different consonants or vowels. Not in terms of phonemes but actual letters.

And yeah, 'bicikli' is actually pronounced more like 'bicigli'
(I'm still salty about 'bicikli' keeping the 'k' but the short for 'lakodalom' is 'lagzi' and not 'lakzi')