(1) not necessary after an on campus screening interview. But, if you want to send a short note expressing continued interest, enjoyed meeting interviewer, etc., this is AOK and might help. Since these decisions are usually made quickly regarding callbacks, you need to be prompt. An email is ok. I received one from a candidate that same afternoon while I was still on campus. In the end, his grades weren't high enough, but it did give me pause because he seemed like a good guy who was sincerely interested in firm/practice and I liked the very quick follow through. Had his grades been a bit higher, I would have given the callback and the speedy thank you would have played in my decision-making.
(2) after call backs, not totally necessary, but doesn't hurt. Needs to be timely, i.e. within one or two days. I don't mind emails; but you should do them within 24 hours since they can be sent more quickly than regular mail. I take a quick look then forward them on to the recruiting coordinator for the file and to our committee. To me, it shows follow-up and a continued interest. Now, if the candidate is so-so or didn't do well in interviews, it won't change anything. But if candidate is pretty good and we are choosing between a couple of people, we will factor in that this candidate seems really interested (i.e. perhaps more likely to accept than others) and that person may get the nod. Formal thank yous are fine also, just try to get them out quickly because there can be U.S. mail delays. I don't think we would choose one person over another because of the email versus hard copy thank you. That's me -- perhaps I'm less formally inclined on this one. But we do note a sincere thank you note and include it in the file. Again, if we have someone who sent a thank you versus someone who didn't and their reviews are similar, the thank you person may get the nod because we think they may be more likely to take the offer than to leave us hanging through the NALP waiting period. Especially in this economy, we need to be careful about offers and most of us are cutting back on class sizes.