It is a bit difficult, because so many different organisations nominate "national champions" each year, but if you limit it to consensus national champions (ie. those recognised by the NCAA, which often includes more than one in any given year) then you are left with four:
6
The University of North Carolina does not have any national championships in football.
ummmmm no
116 national championships since 1895 in football. However most teams don't count their national championship pre ww2!
None
Texas
princeton
1
12
Nebraska
Yale #1 Princeton #2
3 games.😏
Zero