"...so we are a bit time limited so anything that needs sorting needs to be done fairly quickly"
Not going to happen I'm afraid to tell you...
In the first place although it's probable that none of the work will need planning consent, building regs approval will be required for the extension and loft conversion.
As the owners have undertaken the work without consent its very likely:
(a) they had no idea consent was required therefore know nothing about the regs and if they used a builder rather than DIY, he didn't know much more.
(b) If they did know consent was required, why didn't they apply? Very suspicious.
(c) to find out what the reality is, the surveyor will have to examine the alterations in detail and guess at what he can't see e.g. foundations, drainage, insulation, vapour barriers etc. Most surveyors are scared of committing themselves without a lot of support and further investigations.
(d) the alterations will probably not conform but even if they do an application will have to be submitted which means someone preparing drawings and calculations.
(e) Either the council will accept and pass the application (but in relality that is not going to happen) or they will reject and insist on remedial work. They may even insist that the extension is demloished and rebuilt or the roof removed and recovered or altered.
(f) Either way they will have to inspect before a completion certificate is issued. Again, no guarantee at that stage that the remedial work is satisfactory.
You have now spent between 8 and 20 weeks or longer.
Insurance is almost always pointless because why on earth would you buy something which is probably substandard and from a vendor who has knowingly concealed something from you. What else are you likely to uncover?
What happens when you come to sell, you would then be in the position that your vendor is in? Why do that to yourself?
If I were in your position I would stop now and begin looking elsewhere.
Option (4) is the only sane one IMO.