Are you familiar with Euler's equations for column critical load?

where the factor K depends on how the column is secured. For a column with both ends fixes K = 0.5. You asked for the "minimum length" under which buckling is likely to happen - that's where the length is sufficient to makes this a "long" or "slender" column, which generally means L is ten times the diameter. To find the force that can cause buckling for that length use the Euler equation above - you have the value for E, and can calculate I from the dimensions you were given. The answer to the third question may seem evident from the fact that F is inversely proportional to L^2, so if you halve L the force F that causes buckling will go up by a factor of 4. However I think this is a trick question, because if the length is now only 5 times the diameter the failure mode will be crushing of the material, not buckling. So for this you already have the value for the maximum stress it can withstand, and you simply multiply that stress by the cross-sectional area of the column to get the force.