What is the firing sequence of a self-loading rifle or carbine?

Answer 1

It will vary depending on the rifle, the type of action, and caliber. For a .22 rimfire, the magazine is loaded, the bolt operated manually to chamber the first cartridge. The safety is released and the trigger pulled. This releases that catch on the hammer/striker, which is driven forward by a spring. This drives the firing pin forward, striking the primer. The primer fires, igniting powder, producing gasses that drive the bullet down the barrel. The gasses also "blow back" the heavier bolt, which extracts and ejects the fired cartridge. It compresses the hammer spring, and cocks the hammer. At the end of it travel to the rear, the bolt is pushed back forward by it's spring, stripping a fresh cartridge from the magazine, and pushing it into the chamber, ready to fire. Unlike heavier caliber rifles, the bolt is not locked in the firing position, but held in place by a spring.

Heavier caliber rifles are usually gas operated- a part of the gasses from the shot being fired are used to drive a piston to the rear. That causes the bolt to unlock, and move back, ejecting and extracting the fired cartridge, and picking up a fresh cartridge from the magazine as it moves back forward.