Do I have a moisture trap?

It is hard to tell without seeing the compressor or its picture. Here are some example of air filters at the Harbor Flight. Not too bad in price. If you need one, make sure to get one WITHOUT the oiler which lubricates air tools for garage type compressor.

You should drain your tank every time you use the compressor to keep corrosion to a minimum. Cambell Housefeld recommends leaving the drain plug in the open position when not in use so the tank can vent and dry out.

Yes you do. The glass bowl with the drain valve is your moisture trap, the "free" valve at the bottom is a drain valve & is forced into its seated / airtight position when air pressure increases.

Being a tanked compressor, most of your moisture build up is likely to occur in the air tank. located somewhere on the bottom of your air tank will be a knurled thumb screw, this is the air tank drain. Every so often at the end of some painting, rather than let the compressed air drain via you brush or regulator, you should the tank drain - this lets the air out, but before doing so will flush any water out that is sitting in the tank. I have seen many a big (garage) compressor ruined due to lack of draining - pumps have to work continually to make up for the reduced air space & the water corrodes the tank.