Any wifi usage on your X10 will not count towards any data plan usage on your wireless plan. Browse away. Just ensure that the phone is connected to the wifi when you're browsing, watch on the notification panel for a "3G" or "E" or "G" accompanied by up and down arrows below it that are "lit" and not dimmer than the accompanying letters. if the arrows are the same brightness as the letters, that signifies data transfer on the wireless network.
From the Home screen, tap the applications bar. Tap Settings > Wireless controls > Mobile networks. Unmark the MMS & Data checkbox.
that should disable all data from going over the mobile network, just reactivate it when you're done to be able to use data and picture messaging again. Also no social networking updates will filter through to the phone while its turned off.
If those directions work, please let me know, they're directly from the user guide on their website, and I hope they are correct.