Is federal flood insurance required for a non-conforming loan from the bank?

Yes, it would be a requirement, if the property is located within a flood zone. The cost of such insurance depends on whether the location is in a 50, 100 or 500 year flood zone. The shorter the period, of course, the higher is the premium. The lender has no choice in the matter. Federally chartered banks are required to impose the flood insurance requirement.

Yes.

Without flood insurance (and there IS no flood insurance for homes, outside of the NFIP), the loan is completely NOT SELLABLE. That means, you can do "owner financing" and not be required to have the insurance, but for BANK loans, you will still need it.

Read the fine print, please, before signing your contract!

Non-conforming loans are a thing of the past.

if you're in the Federally designated flood zone, yes

bank may also require it anyway, but then it'll be cheap, won't it?

Yes if you are in a flood zone.