Some operators pass the MSISDN (the phone number) in the HTTP header, when the traffic goes through their WAP access point/gateway. All of them don't. Some of them will charge a fee for the info.
It won't happen through Internet access points.
The browser type is in the "user agent" header. Look also up info on UAprof (User Agent profile) using the search function here, on http://www.openmobilealliance.org and perhaps also your favourite search engine(s).