Should I replace 3/4" and 1/2" galvanized pipe with the same sizes of pex?
I see your system design viable and acceptable, however modern practice would dictate 1" main lines, 3/4" sub-lines and 1/2" branch to individual fixtures.  I would run 1" to the manifold.  Depending on the individual length, 3/4" and 1/2" would be run to the fixtures.