I do not and will not mow anything without the property owner or an agent/representative of the property owner approving me to do so. Period. I strongly recommend that you not do so either. The property owner assumes some liability any time someone is working on their property and so to do so without their approval is not a good idea. You'll essentially be trespassing to boot. Would you want anyone doing anything to your property without your approval? Hey, I saw you had a lot of dandelions so I sprayed them all for you...
I have mowed the public right-of-way if front of someone's property at the request of someone else, in fact I do it on a regular basis on one account. The town doesn't mind, and in fact encourages mowing of those strips. I maintain about 1/4 mile of the one in front of my house too. But that's different than going onto private property and doing something without express approval of the property owner or their agent/representative.
I would explain that you need the permission of the property owner before you can enter their property,I don't see why anyone wouldn't agree to having their yard mowed for free, but people are different, if they don't give permission then you have skipped a potential legal nightmare
Ditto what those guys say. Does your city or county have a tax GIS website? You should easily be able to find the property owner. Then you could contact them to see if they would agree to it. Whether they hire you or they agree to let you mow it and the nosey neighbor pay you for it.
Pass. My experience with these is the 2 neighbors don’t talk/like each other. And you become the go between!
Depending on the height , no idea what lies beneath! No different than someone wanting to mow the overgrown neighbor yard, “ because you’re there”. I like @sidemouse idea. Call code enforcement and let them have at it!