Yes, though it appears that some limitations on types of handguns may still be permissible. And this decision is likely to be used to strike down laws which give local officials (other than courts) the right to deny gun permits at their discretion. Barring felons and the mentally ill from possessing firearms is a concept that fell into the common sense department back when the Second Amendment was passed, and this can be found in the writings of some of the framers. Nobody felt the need to mention it in the text of the amendment, and the basic concept will hold up. What is not likely to hold up is laws that allow some local official like a sheriff to independently decide that someone is "mentally ill" or "is a criminal" despite no actual felony convictions, and be the end of the line for that individual's attempt to possess or carry a handgun legally.
Are all state laws regarding at home gun safety locks and gun safes invalidated?
No, the limits of permissible restrictions on storage remain to be determined by future court decisions. However, this decision will force restrictions to be consistent with the individual right to self-defense, which this decision makes clear is guaranteed by the Second Amendment. Storage requirements that significantly impair the effectiveness of a handgun for self-defense would likely be struck down based on this decision, since "we don't have to let you use a firearm to defend yourself" will no longer fly.
Although you may intend "laws" to be a shorthand for "statutes, regulations, ordinances, and other rules", I would suggest that the long form is more accurate when referring to most of the gun-control garbage on the books. Laws are by definition Constitutional; unconstitutional statutes, regulations, ordinances, and other rules are not law; unless they became unconstitutional as a result of a Constitutional Amendment, such pseudo-laws are void from the moment of inception.
Barring felons and the mentally ill from possessing firearms is a concept that fell into the common sense department back when the Second Amendment was passed, and this can be found in the writings of some of the framers. Nobody felt the need to mention it in the text of the amendment, and the basic concept will hold up.
What reference is there to the Framers supporting the disarmament of anyone who would reasonably be termed a "free person", bearing in mind that that category would exclude slaves, imprisoned convicts, fugitives, parolees, and people confined as a result of mental illness or disability. I am unaware of any.