Since you don't know what kind of glue was used,,could be anything from hide glue, to elmers, super glue to epoxy..go slow in your take a-part attempts.
Some of the glues respond well to some heat to soften them, others to heat in the form of hot water. Some like super glue will bind to the natural horn just like it does to your skin and separating the two means nothing short of leaving a (hopefully thin) layer of either one or the other materials bound together still attached to the other at separation.
Acetone will cut many fresh glues but older set up products are a dud. Epoxys the same in many cases.
You might want to just leave it where it is since it's a 'nice old horn buttplate' and should be in position when the wood is refinished anyway as already stated.
As far as the rusty, chunky old butt plate screws that came out of it,,that may be an indication of salt cured wood. Browning was not the first in history to figure that trick out and I've seen the problem on more than a few Euro shotguns of pre-WW2 age. French & Belgian lower grade and mid grades.
If the plate is OK and fits OK,,and the only situation you are trying to 'fix' is the old rust remnants down in the butt plate holes,,I'd simply leave the plate where it is. Then drill the old BP screw holes out as large as I could with it in place. Then plug the holes with walnut or other hardwood dowels glued in place.
Make new screws, which you will need anyway for the butt plate.
The new ones can be of a coarse machine thread instread of a wood screw type. They can be smaller in dia than the old ones, thread totally within the new plugs and yet they hold as well or better than the big wood screws often used. A #10 machine screw size is a good place to start.
They are easier to 'time' also.
Make the head and shank that extends down through the butt plate itself the same as the old screws so as to support the plate as original.