Nothing can keep you 100% safe on the Internet, I have never owned a BlackBerry, so you'll have to wait for another user to help you with the first question.
Can BlackBerry keep us safe when we are surfing in the Internet for Facebook and so?
No. Although this does depend on where you are in the world, such as if you're in the US, everything has backdoors in it. This also depends if you are connected through 3G/4G or WiFi. Although the encryption used in phone messaging is getting better, so are the crypto-analysts at the NSA, FBI or whoever...
How can common men and women keep privacy of their own?
With phones, I'm not sure you can do much apart from installing a VPN client...
However in general, I suggest you familiarize yourself with Tor (The Onion Router). Here are the basic security measures you can take with the Tor browser:
LEVEL 1: Tor Browser installed, running on Windows... (Sigh) = You are still monitored and are most definitely on a watchlist.
LEVEL 2: Tor Browser installed, running on Linux. (Yay!) = Linux doesn't constantly log your personal information, this is the level of security most people will take.
LEVEL 3: Tor Browser installed, running on Tails Linux distro (Uber-Ninja Mode) = Basically the height of security. Tails was built to work with Tor, so almost everything is encrypted and safe. If you really want to be sure, get a USB stick, and cram Tails on it!
Tor Browser homepage