Andrew - the purchase will depend on you/your conveyancer as to whether you are willing to complete. Whilst it is possible in my experience a conveyancer would say No. And if you were buying with a mortgage then your lender would definitely say No as the risk is too high.
Insurance is not something we deal with or can advise on. Any property can be mortgaged but see above re No if unregistered and deeds lost/owners dead
If you are able to prove ownership then yes but if the previous owners have died then the law is a complex one as their next of kin inherit and if they don't have any then it can pass to the crown
I would strongly recommend that you seek legal advice before agreeing to buy the property, not least because whoever is selling it needs to be able to prove title to it