Data plan? Nope, not if you're on wifi. You may want to ask whoever sets up your home router if it automatically assigns IPs or if you need to setup a static IP. I'm sure they can also help you from there.
Oh you hafto edit the saved wifi profile for your home network. Just highlight it and click the option button and then you will be able to configure dns settings and such
If you have successfully connected to your WiFi network, your home screen should read "T-Mobile - Your_network_name" followed by UMA (Instead of EDGE).
Make sure in Options/Advanced Options/Browser tha the Default browser configuration is set for Hotspot Browser