Plumbing – How to remove bathtub drain

It looks like you might be able to do this pretty easily.

To remove the stopper, simply unscrew the top of the handle of the drain stopper, then unscrew the underlying screw in the shaft to pull out the drain cover completely. Then, you'll have the cradle-thing that holds the stopper. You might be able to leave that in place (I grew up in a house that had the stoppers taken out but the "cradles" left in place, and two women with long hair would share the bath. We took turns cleaning out the drain) and place the mesh catcher over it. See this video for a demo (It should be region-free.)

You'll probably want to put down putty or some sort of long screw from the drain to the "cradle" in order to keep it in place.

You need to buy something to break up the rust fusion you have going on. WD-40 makes a variety but there are many at your local DIY center.

I would then tap around the drain. Then get a blunt/dull metal block or chisel and hold it against the inner straps and tap on those counter-clockwise. The tapping (with a hammer or mallet) is probably the key to breaking up the rust bond. You can't just start cracking it hard or you could snap one of the center straps or warp the outside.