Yes, you'd generally need the WEP key. You can always try asking your dentist for the key If a network isn't using encryption, your PDA would be able to connect without a WEP key.
Proxy servers are used in large companies and by some wireless providers and PDA browser makers. They parse the content before it ever reaches your PDA. This can be done for security and web site blocking purposes (by large companies when you're working in their office as an employee), or to speed up and optimize download times in the case of mobile carriers.
VPN= virtual private network. This is used by companies who wish to give traveling or home-working employees access to the company network while maintaining a secure connection to prevent theft of company intellectual property or personel info.
You likely won't ever need to use proxies or a VPN connection for your own personal surfing and emailing.