Is there any bonus for collecting all the rings on a level?
Solution 1:
There is no bonus for having all the rings other than maximizing your points (100 per ring). The only ring-associated bonus is the Giant Ring that grants access to a Special Stage. The Giant Ring requires you to be carrying 50 rings when you finish the level.
Green Hill Zone, Act I has 225 rings (source), and as far as I know you can collect them all.