What concrete aid did Severus Snape offer the Order during his second "tenure" being undercover with the Death Eaters?
A few things he did do that I can think of offhand:
- Probably the biggest and most important was smuggling Harry the Sword of Gryffindor.
- Plant the idea for how Harry Potter was to be moved. It's a little unclear to me exactly how that benefitted the Order or Harry Potter, though; it seemed like a very high-risk plan at best.
- Try to protect Harry while he was being moved
- Protect students at Hogwarts (to some degree) while he was Headmaster, given that they probably would've had an actual Death Eater as Headmaster if he wasn't there. In spite of his tendency to be a bully, he's significantly more restrained than the Carrows and manages to reign them in to some extent (e.g. by sending Ginny Weasley on detention with Hagrid rather than letting her being subjected to the cruciatus curse).
Were there other instances that I haven't listed here? Did he ever try to feed them information through some means? (Obviously, he couldn't directly contact them without risking spoiling his cover, no to mention the fact that most of the members of the Order probably wouldn't have been too happy to see him to say the least).
Edit: I'm particularly interested in his activities during the period covered by Book 7 (i.e. the second time he was under cover, after Dumbledore's death).