At least in most of US states, if a neighbor's tree falls into your yard and damaged your house, it is your responsibility to repair your house, and it is your responsibility to cut away the part of the trees that is in your yard. So insurance company might have some incentive to help you cut down the tree.
http://homeguides.sfgate.com/tree-falls-another-persons-yard-responsible-remove-it-60399.html
http://www.washingtonpost.com/realestate/whos-responsible-when-a-tree-falls/2012/11/02/feece3d6-21c7-11e2-8448-81b1ce7d6978_story.html
2. As for your neighbor said about developer, nobody can help you until we see his sales contract, your local zoning ordinance. I don't know how the developer can cheat your neighbor since the tree's condition is plainly obvious for all to see.
3. Sue your neighbor in court
You currently have no standing to sue because you have yet suffered damage. Nothing has happened other than in your head. The court will dismiss your case.
However, as the previous articles indicate, if the tree does fall, your neighbor will be held negligence because you told him the dangerous condition of the tree and he did nothing. You could sue him for damages and probably will win. Read the articles carefully.