Yes.
Yes- but only from a dealer. You may not buy a firearm from a private seller in ANY state other than your own.
No
No.
No. You can purchase a gun from a Georgia dealer, have it shipped to an FFL licenced dealer in California for receiving, and receive it in California, but you can't purchase a gun in Georgia and carry it with you as a California resident. This is due to California's laws, not Georgia's.
Long guns, yes. Handguns and NFA items, no.
Yes the background check for guns is the same in every state
The only way to do it legally is to have the Georgia resident send it to an FFL dealer in California, then take possession of it through that dealer. Georgia's definition of gun rights and California's do not go hand-in-hand, at all.
Rifle or shotgun FROM A DEALER- yes. You may not purchase a handgun except in your state of residence, and any long gun purchased in another state must be from a licensed dealer (not a private person). The answer to this question has changed over the past several years, at one time you could not.
For a felony or domestic violence conviction of any sort? No.
Yes... I may be wrong about this, but I believe Delaware is one of the states where you must be a resident of that state to buy a firearm from there, although I could be wrong about that.
If you are a resident of Virginia, and not prohibited from owning a gun, you may buy a gun from any other resident of Virginia. This applies in MOST states. If you are not a resident of Virginia, then you may buy a rifle or shotgun from a Virginia dealer, but not a private citizen. This is addressed in Federal law- US Code 18.922