Are you familiar with Euler's buckling equation?
where the factor 'K' is defined by the type of end supports - for both ends fixed K = 0.5.
If you divide through by the cross-sectional area of the column you get stress:
where r is the radius of gyration (ie I = Ar^2)
Given the value for yield stress this lets you find the value L that would result in buckling. Then use the first equation to find the resulting critical load. As for the third question - from dimensional analysis you can see what happens to F if L is divided by 2.