Bentching et. al.

Question

Dear Rabbi Abadi, According to the Halacha,(if you could answer Sephardi and Ashkenazi I would appreciate it)does one have to wear a hat(Ituf)during bentching. In addition, is Mayim Achronim mandatory(Shabbat/and or during the week if that matters). Lastly,leaving a piece of the bread so that the Brocha can rest on it, during Birkhat hamazon, ditto.? I know that these are not cornerstones of the tradition, but are they of Halachic consideration in our times? Thank you very much.