First part to remove would be the knobs and they are usually fastened to a spindle (square rod inside) with set screws. The screws have to be exposed and turned and paint, as well as rust, may make it difficult to stripping the screw (sometimes hex and sometimes straight slot). Functioning mortise locks can continue to work so you may want to use paint stripper to remove much of the paint so you can see what you're doing. There are many youtube videos on these locks. Watch a few to get as much idea of what they are like. Sometimes they are all brass parts and you don't want to scratch them too much.
You can replace them with more modern locks. Patching and repainting the doors. Bed/bath knobs have lock buttons inside and they should open when the knob is turned, without having to unbutton from inside. I think this may be panic escape function regard to fires and such.
You can replace them with more modern locks. Patching and repainting the doors. Bed/bath knobs have lock buttons inside and they should open when the knob is turned, without having to unbutton from inside. I think this may be panic escape function regard to fires and such.