In answer to your questions, flashing is a term used to describe a drywall patch shows through a finish coat if it wasn't properly sealed. It typically refers to a difference in texture and sheen due to a different absorbtion rate and is easily avoided by sealing with something like Guardz or Bulls eye 123.
Back rolling refers to rolling walls right after they have been sprayed to work the paint into the surface and to give the finish that light "orange peel". If you spray interior walls without back rolling it will make any future touch ups more difficult, as they will have to be done with a sprayer or there will be a difference in texture between the touched up area and the rest of the wall.
Back brushing is the same basic concept and it's what i do when spraying substrates that are porous or somewhat uneven. Back brushing eliminates "pin holes" on uneven or rough surfaces (think cedar shingles/shakes and rough-side-out wood siding) and works the coating into the wood fibers. It can also help to even out a coat if your spray technique isn't perfect. I don't feel back brushing is needed when spraying very smooth, non porous surfaces like trim or vinyl and aluminum siding.
As an aside, I know what it is to be unfamiliar with what some consider to be very basic terminology. The guy I learned to paint from didn't use sprayers of any kind so I was unfamiliar with the concept of back rolling and back brushing up until a couple years ago. I had also not heard the expression "laying off" until a few years ago, even though it's something I had done almost every day!
Regarding your sprayer, if you really want to know the difference between your sprayer and a 440i get in touch with your local sprayer repair guy and ask him. The fact is, your sprayer is a lesser machine than a 440i, although just looking at the information you provided, it's probably fine for what you do. It doesn't sound like you do a huge amount of spraying and this machine will probably serve you well for a long time if you maintain it properly. If you find that you start doing alot of spraying or if your current rig kicks the bucket, it might behoove you to look around for a good used 440i or a Graco 390 or 395.
NOTE: these comments represent one guy's opinion