Plumbing – How to remove the tub diverter

It's called a tap connector (obvious now I've found it), and you should be able to unscrew it. You can see one here

It's the bottom nut you need to be turning. It's part of a joint that attaches the pipe to the tap.

Once you have this off you should be able to remove the tap as normal.

If it's stuck then something like WD40 or penetrating oil might help. Failing that carefully heating the nut with a heat gun might expand the various parts enough to loosen them. Take precautions to avoid getting direct heat onto the bath (it appears to be acrylic).

A more drastic approach would be to take a hacksaw to the thread to separate it that way.

Looks like it says "BRASS" on it, I'd guess American Brass. Identify your stem, here.

It may not leak anymore if you have tightened it, but now you need to loosen it a little to let it operate. I appreciate your need to be gentile, but I'd swap the entire valve out. One thing though, is that nipple NPT? It kinda looks like machine thread.

Safest way to take it off is to 'back-it-up' by using a pipe wrench on the nipple and an adjustable wrench on the valve. If you collapse the nipple with a pipe wench, it was about time to swap it all out anyway.

Backing it up, keeps the tension between the nipple and the valve, and doesn't let the rest of the piping spin.

Don't care, just want it to work and not leak: lock it down in the 'on' position.

Small leaks plug themselves. Relieve some of the tension on the packing nut, put a pan under it and see if it stops in a few days.