You would need permission from your neighbour and possibly from the Local Authority.
If it fell in your yard then you can keep it.
Yes, it is their property and the choice is their's for whatever it is they want to do with it.
The question is irrelevant. Peanuts do not grow on trees.
A chery grows on a bush and on a tree. People with a small yard, can plant a cherry bush and enjoy this delicious fruit and the people with a big yard can plant the cherry trees in it.
Nobody is liable for an act of nature. Each property owner would responsible for their own insurance to cover resulting damages and debris removal from their own property.
If possible, you should request that your neighbor trim the branches. If you trim them and somehow the tree coincidentally dies, there would be further problems.
You might want to check your local ordinances (laws). I am pretty sure that a tree that is planted in your neighbor's yard and overhangs into your yard can be trimmed back to the property line. It probably won't make your neighbor happy if it kills the tree though. Just be sure to check the local laws in regard to this beforehand.
You are not required to remove the tree at all. As long as the tree is in your yard and the tree is not in danger of causing damage, you do not have to have it removed.
I would imagine yes but will depend on your local laws. Phone your local council for advice. In most municipalities, the neighbor has the right to trim any branches off your tree that hang over his property--at his expense. Insurance companies expect that homeowners will protect their homes from any tree branches whether they belong to the homeowner or the neighbor's tree
You could try speaking with your neighbor in a friendly manner and ask if you can prune your side of that tree. Our neighbor behind us had no light coming in her window because of one of are large cedar trees. She paid for a tree pruner to come in and we supervised to be sure the tree wasn't ruined. We were happy and she got her light. You could ask your neighbor to join you in pruning the tree. If your neighbor is giving you problems then go to City Hall and ask for their help and also get to know your property laws in your State.
In this humorous twist on "A Tree Grows in Brooklyn," a kooky family moves into a suburb known for its lack of trees. Amidst their comical misadventures trying to grow a tree in their yard, they learn valuable lessons about community, resilience, and the power of nature.
If it's in your yard it is your tree.