Spring guns are notoriously hard on scopes and mounts. The double-action recoil, back then forward, can kill even expensive scopes not designed for them. Mounts will always tend to slide for the same reason. Scope tape helps but the ultimate solution is to install a stop on the receiver to keep the rings from sliding. Unlike a regular firearm, where the stop would be mounted in front of the forward ring, this stop should mounted behind the back ring. Most spring guns, even the cheap ones, have a stop already mounted. Mounting the scope make sure the ring is hard up against the stop.

You are going to find that the barrel will take a couple thousand rounds to settle in fully. Consistency between shots should improve over time even discounting any learning curve.

There is nothing wrong with using oil in the barrel. The key to prevent dieseling, detonation of any oil, on a spring gun is to never let oil get into the hole where the spring is. It isn't oil in front of the pellet that causes dieseling; it is oil behind the pellet where pressures spikes.

Some sort of oil or treatment is necessary to prevent the bore from rusting. Store the rifle muzzle down to keep any oil in the bore from running down into the spring chamber where it might cause dieseling. If you used a heavy coat of oil to protect the bore in storage swabbing the bore with a dry patch before shooting is a good idea. But a tiny amount of smoke or vapor is not an issue. Remember that the spring is compressing air to several thousand psi in a fraction of a second and then releasing it. So some vapor, because air is never dry or clean, is to be expected.

The rifling on a pellet rifle is quite shallow and the steel is relatively soft. It doesn't take much wear or rust to destroy the rifling. So never shoot anything but lead pellets or plastic booted pellets. Avoid BBs in a pellet rifle. The copper coated steel will peen the rifling flat. Also never use a bore brush or any bore cleaner intended to remove fouling. They are much too harsh for the delicate bore.

Cleaning the bore is just not necessary very often. There are no residues from powder. Cleaning can be limited to fire-through wool plugs wet with oil. I had someone show me how to break a Q-tip in half, oil it, and insert it like loading a pellet, this is simply fired into a tin can. Done two or three times the bore gets scrubbed clean, dirt is carried off, and bore gets a light coat of oil to keep it from rusting.

Be aware that from magnum spring guns many of the lighter pellets have thin skirts that can get distorted from the impact of the pressure wave. With a distorted skirt they don't seal well and they fly inconsistently. You can get a lot of random scatter and fliers. If you look at a target and see 'key-holing', where the pellet went in sideways, suspect that he skirts are getting distorted.

The other thing to remember is that keeping pellets below the speed of sound will almost always get you tighter groups. Shooting without the Crack of a supersonic pellet is also a little more enjoyable. Higher power spring guns tend to shoot better with heavier pellets that travel a bit slower.

Unfortunately whereas bullet weight for firearms is easy to look up there is no reliable lists of pellet weights that I know of. A few online sites that sell to dedicated pellet shooters tell you the weight of the pellets they sell but the prices are a bit high and are not the brands most commonly available over-the-counter.

The good news is that pellets are cheap, particularly when compared to fire-stick ammunition, so it isn't too expensive to experiment. The brands that aren't up to snuff are still great for murdering tin cans and general plinking. And if you miss a shot while plinking with your nephew you can blame it on the less-than-prime pellets.