What is the mesh for and what about the drywall

There are many kinds of insulation mesh, all will work fine as their only real purpose is to hold the wool in place until the drywall is installed to cover it all up. That said, the blower works better with netting as opposed to a mesh as it provides an escape path for the forced air. Apply staples every 2-3 inches and cut holes with a knife to make new ones for blowing.