For the sleep study, you need a chest band, a nasal cannula, and a pulse ox.

They need to know how much/how deeply you are breathing, and correlate that with your oximetry. The main thing they are looking for is central apnea, where your body stops trying to breathe. PAP doesn’t fix central apnea, because it’s not obstructive, and in fact it can CAUSE it, especially in people who have had obstructive apnea or pulmonary disease for a long time.

You almost certainly need to see a sleep doctor to get a prescription.

That I don't know. My guess is, probably not.

I do know that, when I had my in-clinic sleep study, the technician showed me how my blood oxygen levels were rising and falling. Rhythmically, corresponding to every breath I took.

If you see the oxygen desaturation for yourself, maybe that's what will convince you to at least do an in-home study.

I will never do another in-clinic study again. I fucking hated it, tons of straps and wires all over. I had a lot of trouble getting to sleep and staying asleep. So, as Bill Clinton might say: "I feel your pain". And they did give me a sleeping pill in the middle of the night to calm me down (another issue of yours). But that was over 10 years ago, I don't think that in-home studies were popular at that time.