a) The magnetic field created by a current-carrying wire is proportional to the current:
B ∝ I, B = magnetic field strength, I = current
The magnetic force acting on a current-carrying wire immersed in a magnetic field is proportional to the current and the magnetic field strength:
F ∝ IB, F = magnetic force, I = current, B = magnetic field strength
Let's focus on wire 1.
Since wire 2's current is doubled, wire 2 produces a magnetic field twice as strong as before.
Wire 1's current is also doubled, therefore we now have a wire having <em>twice as strong a current</em> immersed in <em>twice as strong a magnetic field</em>. The magnetic force on wire 1 (and you can make a similar argument for wire 2) will be four times as strong as before.
b) The general formula for the magnetic force acting on a current-carrying wire immersed in a magnetic field is given by:
F = IL×B
F = magnetic force vector
I = current
L = vector having a magnitude equal to wire length and representing direction of current
B = magnetic field vector
Note we are taking a cross product of the IL and B vectors, not the product of two scalar quantities.
The very nature of the cross product means that if L and B are parallel to each other, F = 0N
