In english if it is a lot of the noun afterwards has to be plural so hats, just for those learning English
Not true in general ("I bought a lot of water", not "a lot of waters"), but true for countable nouns such as hats, of course.
Quantum sapka: can't tell whether it's a hat or a cap until you observe it
If you notice errors, please report them.
Yes you are right collective nouns like water are not made plural. Only bottles of water.
could you also accept "the French have many weird caps" ?