SATA III SSD downward compatible?

I have two questions:

1. I have an old motherboard with SATA I slots. Could I mount and SSD SATA III? Is the hard drive downward compatible with SATA I slot? I wouldn't buy an SSD just to find out the answer is "no"...

2. If I will coect an SSD SATA II or III (via an adapter) to the IDE slot, is there a max limit of what the motherboard can see? (I heard the SSD should be max 250 GB or max 500GB)

Thank you!