Tefillin and Birkat Kohanim

Prayers and Blessings
1

During the weekday, what is the proper procedure for a Kohen with respect to Tefillin and handwashing. What I’m asking is

  1. does the Kohen unwrap his hand Tefillin for washing, and
  2. if 1=yes, can (and should) the Kohen rewrap his hand Tefillin BEFORE giving Birkat Kohanim?
2

Yes
Yes