If I sell one of my properties via "Owner Carry" that I have a HELOC on would I have to pay off the HELOC that I have on this property? And...

Would my buyer's insurance policy that I would require satisfy my lendor's requirement of me having insurance on the property I have the HELOC on?

Seller financing with a HELOCs is an important matter, they are short term financing, they can be adjusted or called almost at the whim of the lender, read the fine print. You will be putting your buyer at a greater risk, as well as yourself doing a Sub-to with that loan, it's much different than an amortized loan and yes, it has a due on sale clause as well.

Insurance can be assigned to a lender as a loss payee regardless of who else may be insured, but doing so sends red flags to lenders that there collateral may have been sold if the primary insured is dropped from a policy. See your attorney and consider assignments of loss proceeds and co-insured agreements. :) 

I don't do sub-2 buys or sell on a wrap when a HELOC is involved. The risk of it being discovered and called due and payable immediately is way too high.