A. Weekly Reports
I think reports could be more often than weekly. I don't see why a
student can't shoot an email to the mentor at the end of every work day,
or work session, with just a brief summary of what's been worked on or
what progress has / hasn't been made. Then these emails would comprise
the "weekly" update already, as long as they're working often enough.
B. Dual-mentor
Definitely agree
C. Questions
I like XBMC's request that with an application come with a proposed
timetable, roadmap, or other sort of information showing that the
applying student also knows (or at least is capable of making a
reasonable guess) as to what steps are included in his project, and the
sort of timeframe it could reasonably take. While not a simple question
in the way yours are, it would help the mentors more readily judge
whether the applicant and the project are suited for each other.