What criteria does a research project need to match to be called open science?
To answer the first question:

I asked a similar question on twitter a while back and got a range of responses.  Those are summarized in a storify.  To paraphrase that summary ...


open access to data
open access to code
open access to publications
open source
work must be reproducible
needs to be web enabled


The last bit, and I think this is an important component, is that open science is not binary.  It occurs along a gradient. 

As for you second question, I would use reproducibility as a guide.  The minimum data that needs to be accessible is that which allows for an anlalysis/project to be reproduced.  Following the gradient theme, you could open up more than this, but that it isn't necessarily required.