The reason for the extremely dry mouth, particularly with nasal masks and pillows, is that a substantial amount of air is leaking out your mouth. CPAP (and BiPAP, APAP, AVAPS and any other PAP therapy) is ONLY effective if the pressure going in "works" on the obstruction. There needs to be a sealed (or very nearly sealed) system. If the air goes in through your nose and the majority leaks out through your mouth you might as well not be wearing CPAP at all. Period, end of discussion.
In regards to drying of the mouth, pretty much a person's entire oral health depends on the oral cavity staying moist. Our mouth is a damp place. Over time, you can develop all sorts of problems if you are dessicating (drying out) your mouth on a frequent basis. Gum problems, tooth problems, tongue problems, buccal mucosa problems, bad breath, etc.
If you are leaking out the mouth, you NEED to get a chinstrap to keep your mouth closed AND your cheeks compressed. The absolute best chinstrap on the market, and I have personally tried them all, is the Ruby from Puresom. I, personally, leak so badly from the mouth that I require a full face mask AND a chinstrap, which is the worst case scenario.
If you're feeling nasal congestion, the most likely reason is that the humidity is not right. Humidity/temperature levels do not fall under the MD Rx and can be adjusted by the CPAP tech. If the humidity is too low, the nasal mucosa can shrink and dry out which can cause bleeding from the nose; if the humidity is too high, the mucosa can swell up causing congestion. CPAP can also affect the sinuses. The perverse thing is that exactly the opposite to the "norms" can occur. For most of my patients, I recommend increasing the temperature/humidity more often than reducing it. As with everything CPAP, you, as the individual, has to discover what works best for you. Adjust the temp/humidity (either up or down) in small increments until you find your sweet spot.
Some people can skip the humidification all together, and it works for them. They are in the minority. The airflow that a PAP machine puts out will generally completely overwhelm the body's natural ability to warm and humidify the air being breathed in. I always recommend my patients utilize humidification with PAP therapy. Only about 1 in 10 folks can comfortably use PAP therapy without supplemental humidification.
Use DISTILLED water in the CPAP machine, NOT bottled drinking water, tap water, filtered water, or, certainly not, well water. There are a few different reasons, but one of the big ones is that good "tasting" water has minerals in it. Literally pure water is supposed to be colorless, odorless, and tasteless. Mineral precipitates are not good to ingest into your lungs and are not good for your CPAP equipment, so use distilled water in your PAP machine and clean the water tank REGULARLY - at least once a week (which is also how often you should be cleaning your mask) at a minimum. It is not difficult! Use a solution of white vinegar and water, allow to soak for 10-15 minutes, drain the tank, then rinse thoroughly with distilled water and let it air dry. If your water reservoir is easy to open up, you can even put it in the top rack of the dishwasher ON THE RINSE CYCLE ONLY! Automatic dish soap is very powerful and can ruin the gaskets/seals rapidly.