Cleaning Globe-Wernicke

I recently became the custodian of 2 Globe-Wernicke barrister bookcases that belonged to my great-great-grandfather. I have several problems with them, since they have been stored for the last 50+ years in an unheated woodshop on the family farm.

I have been told that they are made of mahogony, but have been unable to find any markings to that affect, and the original labels are intact on the cases. Where do I look to find out if it is oak or mahagony?

The first thing I need to address is cleaning, the finish while it looks in fairly good condition is very dull. What can I use to clean the years of dirt off with out harming the finish? The wood is dry and does not seem to have sustained any water damage from it's lack of care.

My next problem is 2 fold. First, from sitting in the extremes of hot-cold for so many years many of the joints are loose. What kind of glue should I use to rejoin them? Secound, there is 1 piece of original glass is missing, is it possible to replace it with glass from a "dealer" who sells Globe-Wernicke pieces, or is it better to just buy regular glass to replace it.