For multiple calendars, it's most likely a limitation of your phone. See
Bug 10099 – MobileSync Multiple Calendars and Addressbooks for Zimbra's position on this. Also compare
Multiple Calendars - PPCGeeks (this buttresses the point that the limitation is in the phone, not in Zimbra). Perhaps with Android 2.2 you'll get this feature.
You could vote for
Bug 8157 – Support calendar and contact folder with Zimbra Mobile and/or
Bug 7256 – zimbra mobile sync should allow you to choose calendar, but I doubt you'll ever see them implemented in Zimbra. Note, though, that a comment in 10099 mentions a possible workaround with Z-Push (about which, search the forums).
I also doubt there's anything in ZCS 6 vs. ZCS 5 that would affect the availability of contacts on the phone. ActiveSync contacts "just work" e.g. on iPhone with Zimbra. But what features exactly are supported on the Evo, whether they need any patches, how to set them up--those all seem like questions for the phone manufacturer and/or carrier. It looks like these people have had mixed success using Evo with Exchange:
http://community.sprint.com/baw/thre...reqsorting=dec
Depending on what you find, and your timeframe for a solution, you might want to investigate Touchdown, Moonrug Mobile, or RoadSync.