NIE PADRON authority (is it an NIE plus?) and Ownership of Property in

They are two different things.  The NIE is an identification document and is required in post offices, and many shops depending on what you are buying to prove your European citizenship.  The second NIE as you describe it is a Padron and is a local document to your adjuntament which you get from your town hall.  This is to show you live (rent or own) in a particular village, town etc.  This is used by the adjuntament to claim a sum of money from the government which they do for each resident.  You will also need it for obtaining permissions and licences for local things such as burning permits.  If you don't have land you may not have needed it yet.

Whether you are earning and paying tax in Spain or not, you need to declare UK property.  I am surprised they did not check this out when you registered at the tax office.  If you are paying tax in the UK you may not need to pay it here but you must declare it.  As you work for IT, you can easily find the rules for taxation on line.  That is what I did.