That gun is in the category often called "suicide specials", though the H&A guns were of better quality than most of that type. The loading port has no gate. They were made so that when the cylinder was positioned with a round under the hammer, a cartridge could not fall out. They were normally carried on half-cock; have no hammer block safety or transfer bar.
The failure of the cylinder stop indicates a broken part in the gun.
Those were inexpensive guns, selling new for $2-3. No parts are available and I doubt you could find any gunsmith to work on that gun since the cost of repairs would exceed the value of the gun. I'm afraid it is a wall hanger, but regardless, it is made for the .32 rimfire, which is very hard to get and expensive.