Is my drone covered by my homeowners or umbrella policy?
It depends on the wording. Many personal policies exclude liability arising from aircraft, and whether an unmanned aircraft counts varies between forms. It is worth asking specifically rather than assuming a hobby drone is treated as a camera.
A neighbor says I flew over their yard. Is that a claim?
It can be, as an invasion of privacy allegation, which falls under personal injury cover where the policy includes it. That cover is optional on many umbrellas, so the answer depends on what you bought.
I take photos for a friend’s business. Does that matter?
If there is payment, yes. That is commercial use and personal policies exclude business pursuits. It needs commercial cover, and it is the most common way a hobby becomes uninsured without anyone noticing.