1. The mask itself is called the GP-5. It was made by the Soviet Union to protect the civilian populace during the cold war.
2. What contains asbestos fibers is the filter, not the mask. The mask itself is safe to wear, but I would recommend just leaving the filter seald and not disturb it. The only thing that could harm you is the asbestos in the filter so as long as you don't wear the mask with the filter on it you will be good.
3. The type of thread used in this mask is a 40mm GOST thread, used by the Soviet Uion and Warsaw PACT countries. These threads are not compatible with modern NATO STANAG 40 mm filters (which are safe). You have 2 solutions. You can buy a modern 40mm GOST threaded filter from russia OR you could just wear the mask with a modern 40 mm Nato STANAG filter. The second method is purely for cosmetic purposes only (meaning that it would not protect you from a Nuclear, Biological, or Chemical threat) as 40mm STANAG filters do not have an airtight seal with the GP-5 or soviet - Warsaw Pact GOST threaded masks.

Tip: Buy a modern 40mm Israeli gas mask which is compatible with NATO 40 mm filters here.