I think you’ll find his “original meaning” is nothing more than good old-fashioned liberal textualism. For him, Constitutional interpretation is a game of searching for just the right combination of meanings of the words to produce the desired result.
Both, but I don't think we'll ever get that toothpaste back into the tube.
"And how do you square non-incorporation of this particular right under section 1 of the 14th amendment with the finding that it's an individual right? Is it somehow different from the other rights?"
There are other individual rights that are not incorporated. The protection of your right to be heard by a Grand Jury in capital crimes does not apply to the states. The protection of your right to a trial by jury in civil cases does not apply to the states. The U.S. Supreme Court has never said that the third amendment applies to the states.
So, no, the second amendment is not "different".
For incorporation, the Court would have to find that some right was fundamental to the concept of life, liberty, or property -- due process would then demand that the states protect that right. It's totally up to five justices to make that determination. I don't know their criteria.