In my mind, "homework" is a kind of "mass noun" like "air" or "bread." It is not an item; speaking colloquially, it is just a bunch of stuff I have to do. In order to turn it into something that can be counted, I need to add other words. I can say "I have two PIECES OF bread." I can say "I have two PIECES OF homework." "Homework" is a noun, but we can use it like an adjective. "Assignment" is countable. "I have two assignment." I can use "homework" as an adjective: "A homework assignment," "A classwork assignment." What kind of assignment? A homework assignment. So I can say "I have two homework assignments." "I have a lot of homework." "I have a pile of homework." "I have too much homework." "I have done some of my homework." ("I have eaten some of the bread.") "I have finished all of my homework." ("I have eaten all of the bread.")

We don't have perceptions of countable or uncountable in our minds, we just know what sounds right according the the grammar. It's simply a question of whether a word in a particular context is singular or plural. 'Homework' is a singular noun, so native speakers instinctively know that 'How many homework have you got?' is wrong. We'd say 'How many assignments ?' 'How many exercises?' , because these are words in the plural. 'Homework' is a singular noun - there is no such word as 'homeworks' - so we instinctively know that 'How much homework have you got?' is correct. So, no concepts, no perceptions, no deep meanings - just the simple grammar of singular and plural.

"I have got homework for Math and English classes." is EXACTLY right. Or "I have Math and English homework." Or "I have two assignments." I don't understand what you mean by "uncountable forms."