I LOVE how airplane builders come up with way to deal with things that NO one else would have thought of! The coiled water remover is genius! May come from their Moonshine days.............
In the 13,000+ rivets that I drove, I did NOT have an oiler as I wanted my hoses to be oil-free. A few drops of air tool oil in the air hose fitting on the tool prior to using them each day was plenty. And likely used less oil. I wanted to control how much oil my tools were getting. I didn't have a pneumatic squeezer but have heard NOT to use oil in them.
I would suggest dedicated hoses for painting. Mine have never had oil in them but would probably have oil hoses one color and clean hoses as another color. You don't want ANY oil, even a miniscule amount, in your paint lines. Unless you are fond of fisheyes. A water filter in line and also one near the paint gun has been used in the past. And primer is paint so that applies to anything you put through a paint gun.
Have fun! Painting can be very interesting! I had some variable experience blowing painting, mostly cars but some on airplanes, and I did all mine myself on both the RV and the Cub; they turned out pretty well. And, when I get to where I am redoing the paint, plan on doing that as well. If a neighbor has a junker pickup or car sitting around, offer to do a backyard paint job on it for practice.
Shooting some test stuff, even on cardboard, will help you get a feel for the gun, settings, painting, technique. Ask your paint vender if they have some paint that was returned or aren't likely to sell of the same type you are thinking of using that you could use for practice.
There are many books and UTube videos about painting. Painting cars is similar, just a slightly different shape. And you likely won't paint anything UNDER the car.....