Glue is likely hide glue. Water and heat are your friend for taking it apart to clean the joints. Personally I would stick with it to reassemble it as well. It's reversibility is what makes it so good to work with.
It may have veneer on the legs, or could be Quadralinearly sawn. You should be able to look at the end of them to determine that.
VeneeredQuadralinear postsFinish is likely Shellac based, so alcohol used in a hidden spot will tell you how easy cleaning the wood up would be, usually it is fairly easy. Bringing it down to bare wood will offer you the best redo, and you can more easily lock those joints together so they don't have that gapping.
A weekend and you could have a beautiful piece, plus once it's done you will look back at it as a fun process where you get a look back at older construction methods, and products, so learning will happen. Funnnnn. :-)