Is "no problem" or"no worries" similar to "that's fine"or"that's okay"？
For instance, one broke my cup.
I told him it's not a big deal
I could say "no problem" or "no worries"？

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Yes those are interchangeable. The one you use usually depends where you live or the familiarly of the person. I would use ‘no problem’ if I knew the person pretty well but they were possibly older, if I was being very polite I would say ‘it’s not a problem.” If I was talking to a friend I would say no worries. If someone breaks something I wouldn’t say that’s fine or that’s okay. I use those to reply to someone in conversation. If a friend broke my cup I would say, “ it’s okay, don’t worry about it.” If someone I didn’t know well broke my cup I would say, “it’s not a problem, don’t worry about it at all.” To be more reassuring that everything is okay.