If a neighbor's tree (s) fall and damages my property are they liable?
I think if they planted that tree and depending on the damage yes and no.
Yes yes yes
Yes it would be there liability. It should be covered under their home insurance... If they have coverage.
It would most likely be your responsibility unless the tree is in poor condition and you had pointed out it needed to be removed. With documentation
If your neighbor was negligent in the care of their tree and the result of their negligence caused damaged your property, they would be responsible.
key word here is "neighbor's" (singular possessive!) it's their tree! they are responsible for what there tree does! ha. they are also responsible for what their dog does...;-)