Uberti describes the firing mechanism as 'inertial'. So, the firing pin extension -- the part the hammer contacts -- doesn't have to move much to impart significant energy to the firing pin. The pin, itself, floats inside the bolt and is retracted by a light spring. If the gun goes boom, the system is working.
The "floppy" trigger is a characteristic of the '73 design. It is a two piece trigger, where the part you put your finger on is separate from the actual sear. It is normal for it to be 'loose' when at rest. It is necessary for it to be this way in order to accommodate the lever safety, which was THE major innovation of this design in 1873. If you want a non-floppy trigger, you'll have to remove the safety. Good luck finding a bonafide gunsmith to do this modification for you. Most won't, and I don't recommend it after using the gun in both configurations for many years. An out of battery ignition on a toggle link is potentially dangerous and almost always expensive to repair. Be happy with this 'innovation' and become one with it!
With regard to the glitchy opening of the gun, Uberti doesn't do the best finish work in the industry and relies on HEAVY springs to make a poorly fitted gun go bang -- in much the same way as does Roooooger, but even more extreme. If you want a smooth operating Uberti, you'll have to hand the gun over to a specialized gunsmith who's trade is slicking these things up. In the hands of one of our master, cowboy gunsmiths, the gun can be turned into a very smooth operator. Get out your checkbook.