Mount TV above baseboard heater

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.

Most electric heaters that I have seen are direct wired. In other words the line voltage wire does not have a box in the wall the same way a wall switch or receptacle has.

You can remove the heater but if there is no box present you should add a "old work" box to terminate the wires in. since there are units active beyond the one you are removing, yes, those wires will need to be reconnected to carry the circuit to the other heaters. The added box will allow a junction box cover to be attached.