Please help: how to deal with insurance company

I have a rental property: one side of a duplex. My side has broken pipe cause the water damage in both side of the duplex. The other side damage is mainly carpet and dry wall. Their insurance company is contacting me for my insurance information. My insurance does not cover that. I do not have other insurance for such loss.

Questions:
1) Is this necessary to give them my insurance information?
2) When their insurance find out that I do not have insurance coverage for them, will them go after me? (most likely will)
3) How to negotiate with them to minimize the my loss?
4) if no good solution, can they go after my rental property (like put lien on my property)?
5) What is a normal procedure for such case in the court?

Thank you for reading, and any suggestions are welcome.