Are they all correct usages?
1) I know so much about our culture.
2) I know quite a lot about our culture.
3) I know very well about our culture.
(2) is fine. (1) is grammatical but doesn't feel particularly natural to me in normal circumstances; instead you can say "I know a lot / a great deal about our culture". (3) seems a bit indignant, as if someone has suggested that you don't know anything about your culture.
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(2) is fine. (1) is grammatical but doesn't feel particularly natural to me in normal circumstances; instead you can say "I know a lot / a great deal about our culture". (3) seems a bit indignant, as if someone has suggested that you don't know anything about your culture. It is not a normal way of saying "I know a lot / a great deal ...".