I am new to DNS and trying to figure this all out. I am confused on how the clients query the DNS to search the Internet. What zone or settings allow this? I attached an image of the DNS tree so maybe someone can help me out. Thank you to whoever helps. Full size image is at http://img101.imageshack.us/img101/5241/dnsri3.jpg
The zones that you show in your screenprint are those for which your DNS server is authoritative (medical.local and _msdcs.medical.local for your medserver - I assume these are just local domains used for your Active Directory).
For queries about other zones it will be configured (unless you have changed things) to refer the query to other DNS servers. It will either be configured to refer queries to some particular DNS server (recursive), or (not really recommended) will be going straight to the root servers and doing the whole lookup procedure itself (iterative). It will cache results (for a time decided by the TTL of the result) and you can inspect these cached queries by expanding the "Cached Lookups" folder. That way another identical query doesn't have to be referred to the Internet (not for a while at any rate).