Suggest you take out the lock and show us a photo of the inside of the the lock with hammer down and with hammer at full ####
The rear screw in the set trigger adjusts the pressure with which the rear trigger strikes the sear arm and needs to be only strong enough to release the sear. That doesn't take much. The screw between the triggers adjusts the engagement of the front trigger that releases the rear one when set. To properly adjust the little screw between he triggers, first set the rear trigger then turn that screw in until the trigger releases. Then back the screw out at least a half turn. Do this with the hammer down as if at half #### you can damage the half-#### notch on the tumbler. Finally, with the lock out of the gun, check the engagement of the sear into the full #### notch in the tumbler. It should fully engage and if there is an adjustment screw, make the adjustment to allow full engagement in the notch then lock the screw with Locktite, nail polish or something similar.
The nipple screws into the Patent breech "Snail". The clean-out screw is probably a metric thread but may be something a simple as a 8-32 machine screw and easily replaced if the slot is messed up. Good luck.