In my BB Curve 8520, only the browser connects with WiFi, the remaining app's, even third part ones connect using the data plan, which is extremely expensive, since its a pay per use plan.
If the apps have settings to make it connect via WiFi only, other than that.. I don't think there's a way to force them to use WiFi instead of the data plan.
You got to have the browser set up to work on WIFI you need to have Hotspot browser on for the WIFI to work. Any site you have looked at with the reg browser and book marked them using the reg data will not work unless you go in to options and change it to Hotspot browser. and your default needs to be set under browser config to hotspot browser to. I ran out of data two weeks ago and I am still using my internet at home to get online with my phone.
Some applications need a BIS/data plan in order to let them work. When browsing on WIFI,
Be sure that you have marked use WIFI hotspot, like some of the posters have mentioned.
Other than that you will need a BIS/data plan to enjoy the rich BlackBerry experience.