Used to have something just like that. Matter of fact believe I’ve still got one. Anyway to answer your questions
Yes the slide cocking mechanism is usually right on top of the gun and is pulled back to put in the ammunition one by one or is opened to fit multiple cartridges depending on the air pistol.
2.I’ve found pump rifles always worked better than spring loaded rifles because I’ve had more problems with all of the parts in the spring and lock part.
More uniform shot to shot velocity. With a pump model, the air pressure can vary depending on how fast you pump and how soon you fire after pumping. OK, it’s not a great difference in velocity, but it’s a variable that can affect your accuracy.
Faster repeat shots. Pull the lever, or break the barrel, drop in the pellet, close the lever or barrel and shoot.
Cabelas carries several models of air rifles and air pistols. I have a Tempest air pistol. You pull up on the rear of the barrel to cock the spring mechanism. Drop the pellet in the end of the barrel, latch it down and you’re good to go.