Final answer:
Gravity assist maneuvers around the sun aren't feasible due to its extreme heat and gravity. The ISS stays in orbit because it's falling around Earth, not towards it. Astronauts feel weightless because they are in free-fall while orbiting.
Step-by-step explanation:
We cannot use the sun to perform a gravity assist because a spacecraft would need to be highly heat-resistant to survive the extreme temperatures near the sun, and because the sun's immense gravity would require an impractical amount of propulsion for a spacecraft to reach escape velocity. The ISS remains in orbit due to its horizontal velocity; it is constantly falling towards Earth but its forward motion ensures it falls around Earth, creating a stable orbit.
The orbit of Earth around the sun can be described by gravitational force alone since other forces are negligible at that scale. Astronauts aboard the Space Shuttle feel weightless because they are in a state of continuous free fall orbiting Earth, similar to free-falling in an elevator or a plane in a steep descent.