Regarding the recent gun bill defeat.

Let us examine the bullet points in your citation.

Not allowing everyone to possess a gun. The right can be withheld from felons and the mentally ill, for example.
None of which suggests that government has any authority to prohibit the ownership of firearms by individuals who are not legally disqualified.

Not allowing guns to be carried everywhere. Laws forbidding people from carrying firearms in "sensitive" places, such as schools and government buildings, remain valid.
And the fact the supreme court went out of its way to specify this means that there must at least be some right to carry at least some firearms at least somewhere in public. Otherwise if the right to firearms ownership did not extend beyond the home, there would be no reason to mention such.

Certain restrictions on the sale of guns. Laws imposing conditions and qualifications on the commercial sale of firearms continue to be allowed.
Which remains to be proven since the defendant Dick Heller did not dispute such matters, meaning there was no reason for the court to address such.

Banning certain types of guns. The Second Amendment does not protect guns that are not typically possessed by law-abiding citizens for lawful purposes, such as short-barreled shotguns. (The Court endorsed the "the historical tradition of prohibiting the carrying of 'dangerous and unusual weapons.'")
None of which suggests that any type of firearm that is currently freely available on the private market can be prohibited from ownership. Certain refinements of methods of operation notwithstanding, all currently available firearm designs are well over a century old.

Outlawing concealed weapons. Laws prohibiting concealed weapons probably remain valid.
The Heller ruling never went into any detail about the legality of the carrying of concealed firearms outside the home.