Colt Army Special. The 1884 is the date of one of the patents used. The Army Special was the immediate successor to the New Army and New Navy series, which was the commercial version of the military Model 1892 series. The Army Special was succeeded by the Officers Model, which was Colt's mainstay medium frame revolver for years.
Now that screw. Do you have or have access to a drill press? If so, put a block of wood on the drill press table. Get one of those stubby screwdriver bits and put it in the chuck. Then, remove the grips, hold the gun left side down on the wood, and bring the screwdriver down into the screw slot. WITH THE POWER OFF, hold the chuck down with the handle and turn the chuck by hand. Try wiggling it back and forth a bit at first to see if you can break that screw loose. If that fails, then likely nothing will get the screw out and it may have to be drilled.
Jim