Many (in my opinion, slimy) manufacturers will implement whitelists in their BIOS. These whitelists list the parts that will be allowed to operate - thereby forcing you to purchase your add-on hardware only from this manufacturer and at their inflated prices. Now, I am not saying that this is the case with HP (I really don't know); what I am saying is that you should be asking HP for the answer to your first question.
Presuming that you have a A/E-Keyed M.2 connector in this PC and that you can use any compatible WiFi adapter, your choices from Intel include:
Hope this helps,