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

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?)

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.

Yes, all of the sentences you provided are grammatically correct.

In sentence 1, you are simply listing the subjects of your homework, including math, science, and English.

In sentence 2, you are expressing that you have a large amount of homework to do every day without specifying the subjects.

In sentence 3, you are again stating that you have a large amount of homework every day, but this time you are providing specific examples of the types of homework you have, such as math, science, English, and Chinese characters.

All of these sentences effectively convey the message that you have homework to do every day, but the level of detail and specificity varies between the sentences.