You betcha. Self defense is a right. Convicted felons who have served their terms, are equally entitled to arms for their defense. Anyone who cannot be trusted with arms for his own defense, should not be out of prison to begin with.
The criminally insane?
See above.
The unskilled?
Unskilled by who's determination?
The state's?
No thanks.
"Felons" and "criminally insane" people are in jail (if those words mean anything). No, of course they should not be allowed weapons; this would make it difficult to keep them in prison.
"Unskilled" people with weapons should take some classes or something. It's not clear what you want the government to do about them, or how the government would define "unskilled".