I always thought that guns jamming was for things getting stuck in the barrel or failing to fire.

Those malfunctions are referred to as a "bore obstruction" and a "misfire" respectively. A bore obstruction during firing is very dangerous, as it results in the chamber pressure exceeding design limits, which may cause a catastrophic failure of the weapon. Misfires are usually due to defective ammunition or a failure to hit the primer hard enough (hammer or striker spring too weak, firing pin too short or the chamber or ammunition having incorrect dimensions).

One, it is a hell of a recoil

Almost all semi-automatic handguns are recoil-operated, including .22 rimfires, which are known for having almost no recoil. Generating enough force to cycle the action is not at all difficult; the major difficulty in handgun design was actually the converse: keeping the action from cycling too quickly. Using a heavier slide and stiffer spring is one option, but it becomes unattractive with anything but low-powered cartridges. Most pistols designed for police, military and self defense, using medium-power cartridges like 9mm and .45 auto use a locked breech action like the 1911 shown here. It and its prototypes were the first to use the tilting barrel mechanism which is found on most pistols today.

The alternative to recoil operation is gas operation, in which a port in the barrel diverts some of the propellant gasses to push on a piston to operate the mechanism. It is common for rifles, which typically use more powerful, higher-pressure ammunition than pistols, but rarely found on pistols. The Desert Eagle is a notable exception.

The .45's recoil is not generally considered severe. Most people find it milder than the .40 S&W cartridge used by the majority of US police today, itself developed as a milder-recoiling version of the 10mm auto cartridge.

Two, it only works if you don't let the gun go backwards, if you shoot, and allow it to go back, the energy of the recoil will be spent by your body, not the slide, thus the slide won't slide, thus you will have to slide manually... Making it very non-semi-auto.

Failing to hold the gun firmly is known as "limp-wristing" and does increase the chances of a malfunction. Most modern pistols will still cycle in spite of it, but the chances of malfunction are increased. Inertia usually provides enough counter force for the recoil to push against.

Also I noticed the ejector also rely on some small machined parts (like the one that hold the cartridge rim), and thus if not made properly will probably fail (the slide will go back but the cartridge won't go back with it, this probably would be the sort of jam that is an actual jam, you would need to push the cartridge out with another object).

This is called a failure to extract. It's a common cause of malfunctions. Most newer pistol designs, including many revised 1911s used a much larger extractor that protrudes from the side of the slide.

And the amount of springs I am seeing around, mean cyclic fatigue failure of the metal probably causes a couple of issues, I think that a frequently fired gun probably more than cleaning also might require frequent change of springs.

Correct. Replacement of the recoil spring every few thousand rounds is a good idea to reduce fatigue on other parts. As the spring weakens, the forces experienced by other parts are increased. This is more of a problem in some designs than others. The Beretta 92/M9 used by the US military, for example uses a tilting locking block instead of a tilting barrel, and the locking block is prone to fail if the spring is not replaced on schedule. Most pistols are less prone to this category of failure, and some would consider it a design flaw of the Beretta.