No, a different key is not required for each, but a key is still required to deploy your app. Under <your project>, Properties…Common Properties…Assembly…Assembly Key File, you should have a reference to a valid strong name key file.
Next point is pretty serious. Marty Wasznicky told me to NEVER deploy from the project; always deploy from the solution…since this is what the BizTalk Appplication is keyed to. A quick solution to this may be to remove the Application from the BizTalk admin console and then deploy it directly from the Solution.
Last point. I'd suggest building and running this on Windows 2003 Server, or a Virtual machine (Virtual PC, Virtual Server, or VM Ware) running Windows 2003 Server. Its a pretty common starting point for most developers however, I'd like to hear from anyone who recommends XP and who's had great success running BizTalk 2006 on XP. I've stayed away from it since I've had bad luck myself and hear about nothing but pain from other's who've tried.