The answer depends on from where one is escaping - an orbit around the earth or from around the sun.

Then is it one time impulse or continuous.

For a one time impulse, one can set the kinetic energy equal to the required change in gravitational potential energy, in this case, to infinity.

Basically one has to calculate the kinetic energy equivalent to the change in gravitational potential energy between some point in the gravity field and infinity (where effectively the GPE = 0).

However, from the problem statement, it is not clear if one is to achieve the kinetic energy instantaneously or continously, which in the latter case would be decreasing as light intensity falls off as 1/r^{2}.

just set the Sum of Forces equal to zero.
Absorbing the Sunlight's momentum pushes the Area away from the Sun.
The Sun's gravity field pulls the mass toward the Sun.
(it is obvious - ignore the planets, ignore initial velocity)

b) Does reflecting transfer more momentum, or less, than absorbing?

c) how thick would aluminized mylar need to be (mass density about 1.6)?