The click was likely the trigger return spring popping out of its well, which the loose trigger bar would seem to indicate also. It's easy enough to reinstall once the trigger assembly is out.
That trigger pivot pin can be a bear to remove. Use plenty of penetrating oil and punch it out from right to left. If you are using a brass pin punch it won't cut it, you need a steel punch here. It won't hurt the frame unless you are careless and the pin can be replaced if it gets marked up. Use a block of wood with a hole to back the gun (and use a soft cloth to prevent scratches) and don't be afraid to use a heavier hammer. You'll get it eventually.
Once the pivot pin is out the entire trigger assembly should slide back into the magazine well for removal. If that return spring is jamming the trigger you might have to reach in with a pick to remove it first. Drive out the pin linking the trigger to the trigger bar, remove the return spring, and you're done.