In essence, contracts are supposed to abide with statutes. But is there a way for a contract to overpower the laws passed by a legislative body? (e.g. Regulation of minimum wage)
You cannot contract outside the law
Statute law, case law, administrative law - doesn't matter: a private agreement cannot oust the power of government.
For your example, if a person is an employee and employees are entitled to minimum rates of pay, then any contract that purports to pay less than that minimum is not a contract. It's a piece of paper that has writing on it that might be useful if you want to make a paper plane or need kindling for a fire but is of no use (and will probably hurt) in court.
Depends on the statute. Generically the answer is "no;" courts will enforce a statute instead of a conflicting contract. However, many statutes either explicitly or implicitly allow contracts to override them in at least some situations. For instance, in the US the Federal Arbitration Act says that arbitration contracts take effect even if state laws ban them.