Files are not a precision tool so they come in a big variation of sizes. If you want a specific size there are numbered drill bits , letter drill bits and fractional drill bits , each drill bit above has a ream to make it exact size but a file is like using a shotgun a ream is a rifle and a tapered ream is a hand gun in my personal opinion.
The very asking of this question begs another couple of questions; namely your use and whether this is the best way to resolve this use.
Chainsaw sharpening files
Come in a variety of diameters in the rough neighborhood of 1/8".
There are two solutions, both of which you've outlined:
1) Brace two studs with 2x4s and mount the tv to that.
This is hit or miss -- stud spacing has to match the bracket spacing, and you need to open the wall up enough to add the new studs and ensure that they are stable and that the metal studs won't buckle.
2) Put a large piece of thick plywood across ...
That style of hinge is generally made from a pair of metal cups and a piece of round bar.
It definitely looks like a good candidate for heat. There will be damage done to the surrounding paint. Either warm the top piece with a torch, or cut the whole thing off and weld in a new hinge. It looks as if there's welding to be done there anyway to re-attach the ...
I have recently encountered the same problem, and realised it's fire hazard deterrent flashing, and very difficult to drill through. A standard steel drill bit will take care of it. £2.50 at local hardware store.