A read of United Saver / Star Alliance award rules on the United (atleast the US version www.united.com) site will address most of your questions.

Essentially just one stopover is allowed and it can be on a mixed *A ticket.
One stopover en route to your final destination or one open jaw is permitted for a flight award on United between the continental U.S. and Hawaii or between the U.S. and the Caribbean, Asia, Australia, Central America, South America, Middle East or Europe. No stopovers are permitted within a geographic region.

I believe (not absolutely sure) a stopover in Europe when traveling from US to Asia will require more miles