Irvine Environmental / Natural Resources Lawyer.
With respect to the Contractor, at least in California, you may still have the right to sue if there was a "latent' (hidden, or undetectable at completion, but discovered later) and less than 10 years have passed. I agree entirely that you should press the insurer. Based on what you have stated, denying full coverage seems unreasonable. The adjuster will always seek the low cost alternative. This answer does not constitute representation of a client, but rather an initial response...
May depend on where you are, but in California, yes, you can file a lien on any private property, but you have to provide a preliminary notice which gives the owner notice that you are doing work at the property. The notice only goes back 20 days, which means you should file it within 20 days of starting work, to cover all of your claim. The owner can also post a notice of non-responsibility, which would bar your lien. The requirements for liens, and the process to foreclose on a lien are...