Do you have a blackberry data plan? See Main Page - BlackBerryFAQ
and the articles on BIS and how to receive email on a blackberry. To use BIS, you must have a blackberry data plan. (Not just your carrier's cell phone data service. It must be the blackberry-specific data service.)
While at the faq, also look the article on using a blackberry with a generic data plan.
The fact that you don't have the web browser tells me you probably do not have the blackberry data plan. The native blackberry browser will not be showing on the device without it. If you have a generic data service (carrier's mobile phone data service), you may be able to use opera mini to access the internet.
See the aftermarket software forum here on these forums. Also see the third-party software list a the faq.
Desktop Manager from RIM (see the faq for download links) is what you need to syn the PIM data bases (calendar, address book, tasks, notes) with a PC.