I'm having trouble finding a straight answer to this. My question is, if Site A redirects to Site B does that redirect from Site A count as a link to Site B and does it make a difference whether it is a 301 or 302 redirect?
No, redirects do not count as backlinks. If you usue a temporary 301 re-direct, them sometimes you can temporarily pass through your pagerank to the sit you are re-directing to, but it's only temporary.
no, why would they they are redirecting to your website, a bot can not scan a redirect as a backlink.
Don't ever use 302 - it can harm your site. Use 301 which help quite (maybe even 50% link juice is saved)