Zohar

Before zimun, should one verbally announce the intention to bentch (recite Birkat HaMazon)?

One should verbally invite the group before Birkat HaMazon by saying 'hav lan v'nevarekh' or similar…

Should the arm tefillin be put on sitting or standing, and the head tefillin standing?

Arm tefillin should be put on sitting; head tefillin standing.

Does morning prayer hand-washing require a vessel (kli), and does it require being poured with human force (ko'ach gavra)?

For removing the evil spirit, a vessel is specifically required.

Is it preferable to daven with the tzibbur even if it means skipping parts of Pesukei D'Zimra, or to daven in order without skipping even if alone?

One should pray in order (al haseder) and not skip Pesukei D'Zimra, as skipping 'reverses the channe…