This door slams with zero slowing down. Is there anything I can do to improve it short of taking it apart, like lubrication, tightening bolts, etc?

Plenty of good thoughts in other comments, but absolutely do not "disassemble" that door closer. There is a heavy spring inside which has a slight potential of causing injury. Even without that hazard, you will never get the spring back in place and the oil refilled.

The installation looks weird and the design of the closer itself is different than I am personally used to. I'm guessing you aren't in the U.S.? Even if you aren't all the basic principles remain the same.

It is possible that the hydraulic fluid has leaked out as others have stated. This is very often the cause of a closer slamming the door. But there is no visible indication of a leak in your picture. If it had leaked out, I would expect there to be stains on the very bottom point that is visible in the photo. Instead, it looks clean and perfectly fine.

The bent arm and mounting point on the door are related, I would guess. The installer did a crappy job. At a wild guess, the factory mounting only allowed around 100 degrees of opening, but the users wanted something closer to 180, so things were fudged. Not the end of the world and never the cause of slamming.

The people saying you need to adjust it are likely the ones who have it right. Fortunately for us all, your picture shows what I am quite certain are the adjustment screws/valves. The two screws on the right hand side, sitting parallel to the cylinder. They are both clearly backed out nearly as far as they can go, this would cause slamming 100% of the time. You can even see that the top one is protruding from the surrounding body of the closer.

Turn those clockwise and see if it helps. I'd start at something like 2 complete turns clockwise on both and then test the door. Keep going that way until the door is closing too slowly, then back one off and see if it speeds up. Remember, one controls the speed from full open until nearly closed, so you have to identify which is which by adjusting one at a time, make sense?