Without seeing the rifle in person this is just a guess... but...
It sounds like it's just a simple trigger and not a set trigger. The trigger is simply rotating on a pivot and is not powered by a spring. The spring tension you feel is most probably coming from the sear spring in the lock. A gunsmith that's competent in restoration work could remove the lock, trigger guard, and triggers (not to mention the barrel) and that would provide a wealth of information. If you decide to go that route... please take pictures! Posting pictures helps all of us learn more. The screw coming in from the bottom just in front of the trigger must have another purpose.
The lock not having a half cock position probably has one of two answers. It's been broken off the tumbler over the years... or more likely the lock was made without a half cock notch on the tumbler. Locks without half cock notches are very common. It's not needed unless using set triggers, which would explain a simple (non-set) trigger being used here.
I would do 2 things before fooling with it anymore...
First, run a rod down the bore until it bottoms out, mark the rod even with the muzzle, pull it out, and lay it along side the barrel with the mark even with the muzzle. If the bottom end of the rod is a couple of inches forward of the breech... it means there's still a charge in the barrel. This will need to be removed by someone who knows how to do it.
Second, remove the lock and check the internals to make sure everything is intact and won't be damaged by further handling.