Actually, it's not so much 'proof of address' per se, but proof that the two of you live at the same address. If you want to send more, you can, lots of people do send lots more, especially if they aren't addressed jointly...I sent exactly six because I had six things spread out over a two year period that happened to fit the bill and were addressed to us jointly.
As for the mortgage question, I don't own a house in the UK, we rent, but the only reason I provided a letter about our tenancy was because it was addressed to us...I didn't send any proof of how much rent we pay, but that was sort of obvious, if they were looking for it, in the bank statements - the monthly withdrawal of our rent payment.
Maybe someone else who has a mortgage and has applied for ILR can answer this better, but I don't see anywhere where it asks you to provide anything about 'proof' of rental agreement or owning your house...