If I learn a character whill practicing one list and answer it right repeatedly, if another list has that same character, will Skritter remember my progress with that character on that list too?
Yes it will. Same with words, too!
Yes, @cnr is right! Progress on vocabulary is tracked across lists. In the new iOS and Android mobile clients you can even peek into lists (“decks”) you aren’t studying yet to preview how many of the words you already know.