No ideas on the gal from work other than best wishes

Re the neighbor. Why does he want the tree cut down? He has every right to cut down any part that is over his property. Let him get a court order if he wants the entire tree down.

If he came on my property I would file a trespassing charge against him and you do have the right to file a disorderly conduct charge re the threats. Even if it doesn't stick it is up to him to prove innocence more than you need to prove guilt. (I know this first hand because of my stupid and I mean dumber than a box of rocks, neighbors )

the saying goes "tall fences make for good neighbors" Are you able to build a a very tall fence on his side

Re poisoning the pup - I can see where that is a very legitimate fear. We had a dog poisoned when my kids were young - very traumatic, I don't know how this could be prevented if someone was bent on revenge and psychopathic enough to act on it.

Good luck and let us know how everything turns out