How to determine if wall can handle TV weight

Yes, OSB or plywood would be a suitable substructure. It will distribute the load and create a stable mounting surface for your assembly. OSB is similarly strong to plywood and can be more uniform, depending on the grade of plywood. Its drawback is its susceptibility to swelling and flaking due to repeated moisture exposure.

Individual boards are less solid as a system and you may end up with concentrated loads. That said, if they're mounted solidly, they could carry substantial weight as well.

The key is that the anchors you use in the substructure need to be adequate to grab sufficiently in only 1/2" of material. Larger diameter screws substantially increase pullout strength.

This is pretty standard double-stud, used in this case to provide some extra support for the framing around your fireplace.

You should install like with a regular stud, and do not try to guide your screw between the two studs. The two studs are probably just nailed together in a few spots, and a screw driven in between them could spread them apart. You want each screw to go directly into one of the studs, ideally toward the center of one. You can also attach to the central (single) stud for your TV mount.

As @bib and @mikes point out, because your mount moves you will want to make sure it's firmly mounted at multiple points. If it can attach across two or three of these studs (not just the two that are doubled up, but spanning the gaps) great. If not, see if your builder can add some blocking to support the mount.