Did the Big Bang happen?

[popeyespappy]

If that's the case then how is it that, if we reverse time, the sun and earth gradually get closer to each other?

No.

If the universe is shrinking then so is the distance between all planets as well, as the stars which they orbit, so wouldn't this mean that earth would be consumed by our massive sun?

The planets and stars within solar systems and galaxies are not currently affected by expansion because at the local level gravity is stronger than the force of expansion.