1) I don't think it is critical one way or the other, as long as you are getting treatment for apnea. If you are taking insulin for diabetes it would be a good idea to let your boss of fellow employees know, just in case you get into trouble with a low BG.
2) As a first try I would get a APAP machine. The "A" stands for automatic pressure control. I would recommend the ResMed AirSense 10 AutoSet machine as the first choice, and the DreamStation Auto as the second choice. If COPD turns out to be an issue, then a BiPAP may be helpful. They provide more pressure, and more differential between inhale and exhale pressure. As a result they can provide some limited breathing assistance, in addition to keeping the airway open. My wife was diagnosed with an AHI of 83 and she uses a ResMed APAP, and averages under 1 for AHI. Here is a package ResMed machine complete with the ClimateAir heated hose.
ResMed AutoSet Package
3) The mask has a vent on it that purges air whether you are breathing in or exhaling. If the machine goes off you will continue to breath in and out through that vent. It is not the most comfortable, and you will wake up fairly quickly in most cases. You will not suffocate.
4) Most people figure out a way to sleep on their sides or back while using a full face or nasal cushion mask. Full face masks tend to be less comfortable, and more problematic with leaks that can be irritating. I would try a nasal cushion type first. The ResMed P10 mask is a common one. There are DreamWear masks that have the hose go over your head instead of down from the nose. Some like it that way.
5) Most machines come with a humidifier and I would highly recommend it. They can also be fitted with an electric heated hose that keeps the air moist without having it condense in the hose (rainout). I would recommend that too.
6) If you have a prescription there are many on line companies that will ship you a machine overnight. However, they may or may not work with your insurance company. The big issue with going on line is that you don't get to try different masks. Getting the mask that you can work with is the hardest part of CPAP. So, you may have to jump through the insurance company hoops. It is unfortunate they are not giving you better service.
I am also diabetic, and I found that using a CPAP has done nothing for my diabetes, despite my ill informed sleep technician telling me it could cure my diabetes. It did not make a difference at all, not better, or not worse.
Hope that helps some. Any questions just ask.