Is Neptune bigger than the Sun?
No, the Sun is bigger than all of the planets put together.
What is bigger than an asteroid but smaller than Mercury and farther from the sun than Neptune and why?
Neptune is further away from the Sun than the Earth. The Sun is 149 million kilometres from the Earth, the Sun is 4.46 billion kilometres from Neptune. It follows that Neptune is about 30 times further from the Sun than the Earth. (If you like the Earth is 0.03 times further away from Neptune from the Sun.)