Yes the half cock is the safe way to carry the firearm. THe hammer has a "notch" for the sear to sit inside that prevents it from tripping the hammer in this position. See the drawing below, it's crude but you get the point.
If you carry the firearm in the hammer down position the hammer is actually resting on the firing pin which is resting on the primer of the cartridge. A slight bump can fire the round. THIS IS NOT A SAFE POSTIONS AND ACTUALLY QUITE DANGEROUS.
In order to remove the rear sight you will need to have it drifted out of the dovetail with a punch and hammer. However, you may not need to remove it if you opt for a compact scope with a small objective. Which is what I would put on it if I were going to mount a scope on a lever rifle. I'm not sure what you mean by "loop of metal with a post" but the front sight should be removed in the same way.
Yes the trigger can be worked on to give you a lighter and crisper pull but DO NOT attempt this on your own.
