没有 (méi yǒu) is the everyday word for 'not have' or 'there is no' and also used before verbs to say something didn't happen (past negation). 无 (wú) is more formal/written and appears in fixed phrases; 非 (fēi) is even more literary and often means 'not be' or forms negative prefixes. For HSK1, stick with 没有 for all basic negation of existence and past actions.