In Ontario, years ago, they would just accept what you wrote down on the application and charge tax on it. Now, they charge you tax based on the higher of what you paid or the average wholesale for the most recent period (if there are records).
With old bikes (unlike used cars), they don't have very many, if any, records of wholesale dealer or auction sales. And they realize that many 30 year old bikes can be $150 basket cases which you are going to fix up so they are not surprised when a person buys a bike for so little. They then collect the same 13% on the parts and materials you buy to restore it, and 13% on any labour if you get a shop to do the work.
So, it is important, if work is done or parts are bought before you take possession, that the new owner pay for all that separately and then legitimately give the PO what he will net out of the deal = total cost minus any parts and labour.
I wouldn't write down zero, since a frame with a title has a value ($100 maybe?), even if there are no other parts on it.
As to insurance, I doubt many of us will pay extra for fire and theft etc. when all you need to ride a cheap old bike is 3rd party liability. Self insurance pays off on average and I have always figured it was worth the risk on any vehicle worth less than $2k or $3k.
I'm not sure if homeowners' policies pay on vehicles that are not insured for fire under the vehicle policy. But, if they do, and if you can demonstrate with purchase receipts and photos that the bike had new tires, expensive upgrades/accessories, etc., that it would pay based on the value of the loss regardless of how little you paid prior to upgrading and fixing.
