When the nuclear fuel in the sun is gone, the sun will collapse to a

a. black hole
b. white dwarf
c. supernova
d. neutron star

My answer: I think its a black hole.

If the mass of the Earth were suddenly doubled while the radius was unchanged, your weight would be?

My answer: increased by a factor of two.

How would the earth move if the sun were to suddenly vanish from existence?

My answer: move in a straight line tangent to its previous orbit.

A satellite is moving at a constant velocity around the Earth. The net force on it is?

My answer: It would be directed toward the Earth

The first is wrong; The mass of the Sun is not great enough, however it will shrink, and be white.
The others are ok.