So I managed to complete the "Sewers" level on normal difficulty; the game said "Pixel level unlocked", then I quit.
Next time I started Puddle, my saved game was lost; I could only restart from scratch (this time on max difficulty).
Does this mean that later levels are only accessible on "Extreme"?

OK, I'll answer myself: yes, higher levels are accessible only on "extreme" difficulty. I managed to complete the game and, well, at times it was very hard and frustrating. Actually, it's only what I perceived as a misjudged calibration of difficulty that prevented me from enjoying the game to the max. I found some levels on normal too difficult, and some on extreme fairly easy indeed! I can't figure out why they didn't make all levels playable on normal, and leave the extreme setting to those that are looking for a really tough challenge, and enjoy such things. A pity, since the game is original, inventive and varied, well made and polished, and actually fun when it's not pointlessly punishing.