1) Your mass is your own characteristic, it wouldn't change if you left Earth.
2) Your weight is the force with which you press on the surface. By Newton's Third Law this force has the same magnitude as the force with which the planet presses on you. Denote your mass as m, the mass of Earth as M, the mass of Planet X is given to be M also. Denote the radius of Earth as R, then the radius of Planet X is R/2.
And gravitational force on the surface of Planet X will be 4 times greater than on the Earth's surface by the Newton's Law of Universal Gravitation:
on Earth: `F_E = G*(m*M)/(R^2)`
on Planet X: `F_X = G*(m*M)/((R/2)^2)=4*G*(m*M)/(R^2) = 4*F_E.`
Of course 4*120lb = 480lb.
3) Again, by the Newton's Law of Universal Gravitation, your weight will be
`F'_X = G*(m*M)/R^2 = F_E.`