Rental - Do I need NIF?

Firstly, what is NIF and secondly, we were planning on spending 6 months in Madeira during the winter. Our friends who are ex pats living over there, put us in touch with a local 'estate agency' rep called Rosa. She showed us several properties that she could rent us and her rates were very competitive. We put a deposit on a traditional house but later had to cancel as we were depending on the ferry running from the mainland to get our dogs there, no we don't want to fly them. We are now looked ng at renting in Portugal.
Regards....

Yes, I believe you need a NIF and a bank account to rent property here in Portugual. In order to get the NIF you will need a citizen who will sign for you.

Agreed

This is incorrect - to get a NIF all you need is to present  yourself,  passport & proof of address (address in any country is fine) at any financias office and they will issue one to you free of charge.

Remember that on 1/1/21 things will change as a result of brexit - you will no longer be able to spend 6 months in the schengen zone. The max allowable period will be 90 days in any rolling 180 day period & your passport will be stamped in and out of the zone to accurately record the length of your stay - overstate & you will be denied entry in the future.

I thought that part of getting an NIF required a Tax Representative

You can get a NIF online using a company like anchorless. They were excellent. I got my NIF in about a week. You need the NIF to open a Portuguese bank account. That took about 3 weeks. Note that anchorless emails you the pages you must sign and you have to mail those signed originals back to Portugal so they can complete the account opening. You are supposed to print out the pages emailed to you on A4 size paper.

Through NIFportugal.pt I got my NIF online in 3 days. Online I prepared also everything for the bank-account opening and when I arrived in Portugal, next day I went to the Bank and signed the documents and 3 days later I could transfer money. The document signing procedure you can also do online, but I liked to meet the bank employee/manager.NOTE: for your document-transfer, the camera of your iPhone is good enough, but from your computer probably not.