I think there are many stuff on the web that meets some of the requirements for "probashi" people. I'll list some of them here, if u know some other that is not listed here, please add them.
I'm not including the news paper sites. just mentioning that these are available: Prothom Alo, Ittefaq, Janakantha, Daily Star, NewAge, Independent, manab jamin, Jaijaidin and many others.
here is some other:
Unma Bangla Fun Magagine.
Sargam Music Magagine.
Rashsho Potrica Monthly magagine by Seba Prokasoni.
Somoy Prokashoni Some free PDF bangla book.
Channel I Watch Channel I (for a while at least).