I am answering your questions one by one:
1. All connections would work fine on your Blackberry to the extent of Calls and SMS.
2. The default email client and the default browser would not work without a BIS plan.
3. Since the default browser would not work it will very difficult to install apps. Since most of the apps require access to the default browser for installation and download.
4. You can use WiFi and EDGE for browsing on an alternate browser such has Opera Mini and Bolt. But its not a pleasant experience in my opinion. Both are very laggy.
5. To use apps like Gmail, Google Maps, IM+, Skype, Nimbuzz etc etc you will have install them thru the PC Suite for Blackberry phones and will have to search for special Non BIS versions (especially in case of Gmail and Maps) on the internet to make them work on regular EDGE. This is a very "tiring" experience.
In short, if you want to really enjoy using a Blackberry you must get Blackberry service. Otherwise, it is of very limited use. I bought a 8310 about an year ago since at that time no proper and decent quality QWERTY cell phones were available for a cheap price. But now you do have so many options. Like Nokia C3, Nokia X2-01, Samsung Chat etc etc. I suggest you go for one of them if you don't want to avail BIS. But if you plan to buy one anyway, let me know and i'll give you the non BIS versions of Gmail and Google Maps, i "may" have them.