re: Tree fell - who is responsible?

The part that is on your property is on you now.

If it did enough damage to warrant an insurance claim then the insurance might try to get money out of their insurance, but you would have nothing to do with them fighting that.

You would have had to have documented evidence of neglect on the other homeowners part for them to be responsible and even then, it's a tall task. If it's just a fallen tree with minor damage (possibly fence), you're just going to have to do it yourself/pay to have it removed.

A few months ago I had my neighbors tree fall on my brand new truck. Didn't even bother talking to the guy about it, I just filed a claim for the repairs to my truck, cut the tree up and got over it. It's frustrating, but there's not much you can do about it.