There should be no restrictions whatsoever, except the limits that automatically exist in natural law.
- Age minimum requirement to buy firearms/weapons - there can be no chronological snobbery in a free society, either you are a self-owning adult or you're not. A child can become a self-owning adult through the process of legal emancipation by jury, or by default after reaching a certain age (i.e. 18). An adult can lose his self-ownership by failing to respect the rights of others (i.e. free market prisons) or demonstrating oneself incapable of functioning as a self-owning adult (i.e. mental illness). Thus children, the insane, and convicted criminals (who are yet to pay off their restitution to their victims) have limited rights, which include the right to life and to emancipation, but don't include the right to own property - their parents / guardians / caretakers own all property, including the clothes on their dependent's backs. An adult may choose to allow his dependent to buy something on his behalf, even a gun, but the adult bares the responsibility for it, and selling something to a dependent without his guardian's permission is a violation of the guardian's natural rights.
- Convicted felons and certified crazy people temporarily banned from firearms/weapon ownership - once again, either you're a self-owning individual or you're not, and people who are "certified crazy" shouldn't be free to own guns, forks, or even shoelaces unless their guardians explicitly allow it. There shouldn't be any laws against prison guards giving their prisoners AK-47's, just as there shouldn't be any laws for making 2 + 2 add up to 4, common sense should suffice. Once you prove that you have paid your restitution for any past crimes and can be trusted to respect the rights of others in the future, you're free to own anything you like again.
- Ban on certain firearms/weapons - this is a property rights issue. Property owners should be free to ban anything they want to ban on their property - if you don't like the rules, go somewhere else. Most neighborhood associations, local business alliances, road co-ops, and other privately-owned building blocks of a free society would have charters and other contractual standards for what is and is not allowed in their jurisdiction. Furthermore, if you may be storing potentially dangerous stuff on your property, your neighbors and anyone else who owns property that may be affected have a right to sue you, which would make nuclear proliferation utterly impossible in a government-free society.