Because it's right before autokat and part of the same noun phrase - adjectives before a noun (attributive adjectives) don't get marked for number or case, and milyen works like an adjective in this respect.
I would like to point out that in university-level English, the following are (or used to be) standard:
1. what type of car
2. what types of car
In other words, it is the word before the 'of' (type/kind/sort) that is singular or plural, whereas the word after the 'of' is singular regardless.
That used to be the standard, but nowadays you see plural after the 'of' quite frequently. In fact, the tendency is to use a double singular (kind of car) vs. a double plural (kinds of cars).
I don´t get what part of this sentence indicates that you are looking for carS instead of a single car. Isn´t "Milyen auto látsz" also correct?
Autókat is the plural accusative of autó. The -k marks it as plural, that's why you are looking for multiple cars.
Your sentence is incorrect. Autó needs to be in an object case here. "Milyen autót látsz?" - "What kind of car do you see?"