1

would this be 〜なくていい?

I don’t have to study - 勉強しなくていい?

2

That is correct.「~する必要はない」(lit. "There is no need to (...)") or「~しなくても大丈夫」(lit. "I'll be fine even if I don't (...)") are some alternatives. They have different connotations, so which one you would want to use depends on the actual detailed context where you would use the phrase.

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