'Mog, the pressure from your compressor should be adjustable, I run mine fairly low (at about 15psi) for general use & even lower (down to 5psi) for very fine work.
I find a full clean of the airbrush is not as necessary as many say, mine gets a good wipe out & flushing with thinners.
First, empty out the excess paint, tip some thinners in, give it a good scrub with an old paint brush, pour out the now filthy thinners & wipe out the cup with a soft rag or paper towel. I, then, use the paint brush (wiped on some paper towel to remove the residue of the previous effort) to clean the needle (through the cup, with some thinners, repeatedly pulling & releasing the trigger) & a cotton bud/Q-tip to clean the nozzle (for that I part-fill the cup with thinners, start running the thinners through the system, wet the cotton bud with the thinners & wipe around the inside of the nozzle shield), it bubbles back into the cup & I find it better to tip the last of the thinners out to stop some of the crap that usually comes back going through the airbrush again, then giving the cup a good wipe out & spraying a squirt of IPA into the cup & running the airbrush empty.
I usually strip it down & clean, polish & oil it about once every 6-to-12 months, depending on usage.
Paint thinning is a personal thing & every paint brand is different but, once you know what paints you prefer & what thinning ratio works for you, they tend to be very consistent.
Anyway, there are a lot of very good videos out on the interwebs by people better than me that I suggest you have a look at some, & pick & choose what works for you.