Can all the rings be collected before the end of the level?
Does anything special happen if you collect them all?
How many rings are on the first level?
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.