1. I do math, science, and English homework every day.

Question

2. I do much / a lot of homework every day.

3. I do much homework every day such as math homework, science homework, English homework, Chinese characters homework, etc.

(Are they all grammatical?)

Answer 1

Technically, yes, but the first one is best.

#2 would read better with "a lot" rather than "much."

#3 would read better if you rephrase thus:
I do lots of homework every day, including math, science, English, and Chinese characters.