It would help to know what carrier and phone you're using...
But most likely, No mobile browsing, just social networking sites (Facebook, Myspace, Twitter, etc) but if your phone is wifi enabled then you could browse the web that way.
Well you have the wifi so you can use unlimited over the wifi network but Rogers has really strict data plans so I don't think that you have unlimited browsing over the network. I would just call them and they could explain everything that you can do with it.
Unlimited mobile browsing is not unlimited data, but....
Rogers is offering 6gb for 30 a month, but only for a little while, so if you are concerned about data, then I'd get that plan.