Dreamhost can’t register or receive a transfer of .biz; only .com, .net, .org, and .info.
But to answer your questions:
- The whois entry only matters in that you need access to that email account.
- Auto-renew doesn’t matter, AFAIK. It’s new registrations that matter.
- You’ll need to get the Authorization Code from your current registrar to initiate the transfer.
- But, as I said, DreamHost can’t register a .biz domain, though it can host it just like it can host any other TLD.