The guy that came out to estimate the damage should've included it in the quote IMO. The hose was damaged, therefor it should be fixed... different builders do provide different services i suppose.
If they're frayed, I'd certainly consider replacing them.
No, read your pds. Insurance repairs resultant damage, not what caused it. It has always been that way. It isn't a rip, insurance isn't a handyman service. We used to assess and repair $500k+ a month of insurable damage. If an oven shorts out and burns down your house, you'll be paid out for everything except the oven - you fix that.
Buy flex lines from a plumbing supplier and you'll have much better results than if you buy them at the green shed.
Why did the door fall? Insurance needs to be linked to an insurable event. If some clown under specified it or it was poorly installed by a weekend warrior for example, it won't be covered. It is my experience as an assessor and a builder that doors don't 'just' fall down.
Lastly, insurance will remove a tree if it falls through your home and you are insured. This info is all in the pds. How the hell do you decide what insurer to go with if you don't have a clue what is being insured?