Neighbor's tree fell on my property

What is the name of your state? FL

I have two questions :

1.) My neighbor's Oak tree fell on my property last night resulting in damage to my fence and to my roof - this is not as a "direct" result of any storm. They are out of state and can not be contacted. I called my insurance company to notify them and ended up speaking to an overseas CS rep, but will not be able to talk to my agent until Monday. Also, I had the local police come by and filed a police report, and took "film" pictures so the neighbor who is very difficult can not try to blame this on me.

Whose insurance pays for this mess ? If mine does will they subrogate for my deductable. Can I remove the tree from my property and make repairs before the neighbor returns ? I have no way of knowing when they will return. Even if they do come back it could be months before an adjuster even shows up with the 4 hurrricanes we have had this year.

2.) There is second oak tree that is on the neighbor's property close to my fence line about 10 feet from where the other Oak fell last night. This Oak has one trunk that goes up about 15 feet on their property and then splits into 2 large branches that hang over my house and pool enclosure. It appears to be growing at a 45 degree angle and is about 40 feet high. If I cut this Oak back to my property line or top it off, it will basically kill the tree. If this one falls it will do massive damage to my house. The city in which I live gave me a verbal OK to cut it back to my property line as it is not a "Grandfather Oak" , but stated they would not get involved in any civil action if one arises.

How would you proceed if the neighbor gives me grief about wanting to cut it back to my property line ? If I do cut it back and they sue, what is the likelyhood that they will prevail ? Any other legal tactics available to me ?

Ferenc said:

Do not cut back on the second oak, as it will damage the appearance,
and increase the likelihood for more injury if a storm, disease or something crops up. Instead, you can cable and brace the second tree, which will be much more effective in the long run; Plus it costs less.
As with the first one that fell over, you can get the mess cleaned up left behind by the tree, then when your neighbours arrive, ask them to pay for at least half: respectively. If they refuse, sue them.

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No appearance to damage - even city says it's unsightly. Arborist says not enough room to brace correctly as it is part of a cluster of spindley oaks with a very poor root system, and would cost way too much - cheaper and better to cut down. Can anyone here answer my original questions from a legal perspective ?