I've noticed while reloading that there are two different reloading animations for most guns. One is the normal one, and the other one is a slightly longer one that occurs when you completely empty the gun, meaning that you have to put a bullet in the chamber by pulling a lever or something. If you learn the normal animation, then you can bypass the extended one by knifing, switching weapons or in some cases shooting that weapon and it will still be reloaded.

Yep, rainbow six has also been doing this for a long time. In those games you could give yourself a slight advantage by having a bullet already in the chamber when you insert a 30/20/5 round magazine. Although in CoD4 it doesn't keep one in the chamber to up the bullet count by one.

I sometimes noticed that when I start to reload and then start sprinting after that when I stop sprinting the gun is reloaded.

Yeah, it's somewhat a glitch, and and somewhat not. Technically, with any gun you replace a magazine and you still have a bullet in the chamber that's it. The weapon doesn't need to be re-chambered (re-cocked), but if the weapon has an empty mag and no bullet in the chamber, then you will need to charge it with every fresh magazine.

This holds true in the game, since as soon as you see the magazine fit into the weapon, click the sprint do anything else to cancel the animation your weapon will have a full magazine. Helpful if you need to exit a covered area ASAP.