There is a .44 American Bulldog in the EE right now @$1795. With that kind of pricing, repairing the issues with the OP's revolver makes sense.
thats rough, even at the price of $1790 depending on the repair cost and what the OP paid my guess is its not going to be worth it, the damage looks more like hammering than wear or filing, having 2 of these and both required work firstly the hammer pin scrape is likely the small lifter that moves the hammer back to clear the next round I had to hand make, took several until I got mine right, just takes time and a little at a time. even better if you have a second one to copy but of the 2 revolvers little can be exchanged due to how they were manufactured back in the 1890s.
the cylinder could be bored on a lathe, a new steel plug pressed in and then the teeth recut, problem is where does one cut the teeth, I repaired both of mine but not even close to this bad using tig torch and good steel filler, little at a time, once built up couple hours filing to get it just right, make a jig that the cylinder bore mounts and a rest for the file to guide it, this way all teeth are located the same.
in this case I would tig the best tooth left in place, file and fit to get it right, once happy build up the other 4,
if it were me it would be going back to the seller unless heavily discounted, one could easily spend 4 to 5 hours making the lifter and the cylinder another 10 by the time its working.