Removing hose tap/faucet from old hose pipe (outside) when half the metal thread is stuck
With the new photos added we can see you're working with a regular 1/2 inch coupler on the end of a piece of pipe. Both are probably "black" iron pipe (as opposed to being galvanized pipe).

I suggest removing and replacing the coupler. That'll probably be easier than cleaning out the internal threads. You'll need a pair of pipe wrenches, and heating the coupler with a torch could help too.

For reassembly, apply a pipe thread sealant on the outer/male threads. The white teflon tape is a common choice but my personal preference is usually a paste compound (often generically called "pipe dope"). Being wet it's a bit messier than the teflon tape but in my opinion it lubricates better for assembly and it seals better too.