Making du’a after salah is not Sunnah if it is done by raising the hands. If du’a after prayer is done without raising the hands, there is nothing wrong with it.

There are various versions of the Tashahhud. The view of the majority of jurists is that you should only recite the Tashahhud as far as the Shahadatayn, and not add the blessings on the Prophet (peace and blessings of Allah be upon him).