To delete your messages, highlight the first one then use the shift key and roll the trackball. Or you can highlight a date and select "delete prior." There is a user's guide on the CD that came with the device that will tell you how to do all this.
As far as the wifi, we'd need more info. Do you have a BB data plan with your carrier? You need that to get the green check. Without a BB data plan you can still use your wifi but you need to set the default browser to wifi browser.