Weernink's lovely book "Lancia Flaminia details of the collection" says 165 tyres were only fitted to very early models and that rear wipers were dropped after two years, suggesting 1959. The book looks a bit lightweight in my opinion, given the image on the front cover, but I've actually found it very detailed and informative.
As to 175 increasing the final drive, I thought this was the width of the tyre so wouldn't affect the rolling radius, however, Longstones quote both their 165 and 175 tyres as 80% aspect ration which, if accurate, would make the 175 slightly wider overall diameter.
Disc brakes are part of the 1961 model upgrades.