And why kolory doesn't change in "Mieszamy kolory".
mieszamy requires 'accusative' (biernik) - and accusative of kolory (which is a plural of a masculine noun) happens to have the same form as 'basic' - 'nominative' form of the noun - this is for all nouns in plural actually - except a class which is called 'personal masculine' (personal masculine is for example names of occupations/professions/positions held by males - Polish distinguishes robotnik from robotnica, lekkoatleta from lekkoatletka - the former are masculine the latter feminine (robotnik - worker/labourer, robotnica - femala worker, pracownik - employee, pracownica - female emloyee)
ci pracownicy - these employees te pracownice - these female employees
widzę tych pracowników - I can see these employees
widzę te pracownice - I cans see these female employees
(widzę requires accusative case just as mieszam(y) does - you can see that for "pracownicy", a masculine personal, accusative does not have the same form as the 'nominative' (basic form) (but accusative is equal to genetive in this class)
in general youprobably already noticed that Polish declination system is pretty irregular (unlike Hungarian as far as I know - though maybe there are languages with even more irregularities to their declination)
now prepositions - 'z' is preposition in Polish require specific cases as well
'z' is a bit problematic here because it actually has at least 2 basic meanings
the first is 'z' = 'with' and it requires 'instrumental' - it is often described as a question - z kim/ z czym? with whom/ with what?
the other meaning of 'z' is - out of, from (sometimes off) - this is the case here - z kranu - from the/a tap (out of the/a tap) - this one requires 'genetive' kran, z czego? - z kranu?