Would you agree to a mandatory requirement that a gun safety pamphlet be supplied with each gun sold? It serves no purpose, so I see no need for it. If a manufacturer wants to include something like the Four Rules in the instruction manual, that's not a bad thing, but I see no need for a government mandate.
Instant background check? I'd like to prevent certain classes of people - illegal aliens and minor children, for example - from buying guns, but if you're an adult and are free, you should be able to buy a gun.
Is it OK with you if violent felons have firearms? Violent felons belong in jail. If they can't be trusted with a gun, they can't be trusted to run around loose.
How about the crazy dumpster diver that lives under the bridge? Define "crazy." Unless he's committed a crime or shown himself to be a threat to others, yes.
Can children bring guns to school with them? Generally, no - children are not just short adults, and there are valid reasons that they are restricted from some adult activities, including drinking alcohol, voting, etc. Some age-based restrictions ARE appropriate. Most of these ought to go away once the "child" is old enough to vote or serve in the armed forces.
How about if violent felons have firearms while in prison? Prisoners have few rights - they're being punished for their actions. So this is a resounding no.