I shall try to cover the various queries in this post as succinctly as possible, but I may get lost. CPAP is supposed to lower AHI, but the AHI on your download will rarely be zero. On a download, and AHI of 5 or less is generally considered good because of the the machine measures data. It detects events using only pressure. If your are breathing well, the pressure fluctuation created by your inhalation and exhalation is very regular. When it changes at all your CPAP machine is inclined to count this an event. The manufacturers say that they have some fancy software to refine things, but generally speaking, if your breathing changes they count it. Now, this may be due to an apnoea or hypopnoea, but it may also be because you cough, roll over, twitch or anything else which causes a slight change in your breathing pattern. For this reason, the AHI stated on a CPAP download will always be an overestimate and so most people will never get zero, which is why we have the idea of anything less than 5 being OK. People with Periodic Limb Movement Disorder (similar to restless leg syndrome) will almost always have a very high AHI because they twitch a lot. For this reason they can't use an auto CPAP because it thinks the twitches are apnoeas and maxes out the pressure in an effort to stop them.
In a sleep study, apnoeas and hypopnoeas are detected by a range of sensors. It involves a drop in air flow (detected by nasal pressure and a thermister) accompanied by a decrease on oxygen saturation (detected by an oximeter) or a change in brain activity (measured by an EEG). This adds up to a bare minimum of 4 wires. However, in order to classify the type of event, the effort of your breathing muscles is measured (requiring a strap around your stomach, chest or both which is cheerfully called an inductance plethismograph - say that without your teeth in). This allows us to tell if the events are obstructive or central. Limb movements should also be measured on order to eliminate changes in breathing which are caused by leg twitches (as mentioned above). Overall, this is a lot more detailed and sensitive than just using air pressure as a guide, so this is why a proper sleep study is always considered more reliable than the download data from your CPAP machine.
OrphanAnnie, I am rather surprised that your technician told you that the data your machine records is too complicated. The software can be a bit of a mess, but the data is quite simple and not that hard to understand. I can only suggest that you call the hospital, speak to someone else who works at the sleep lab and ask them to explain the results to you. Having said that, there's not much to explain from a download, but they should still be able to answer your questions about it. That's what I do all the time at work.
Regarding your sinus problems, it will probably affect which mask you use, whether you use a humidifier and such, but it is totally independent of your sleep apnoea. Your sinuses are between your nose and mouth, but obstruction due to sleep apnoea happens at the back of your throat, so they are in separate parts of your head.