"Safari can't find the server" error coming up frequently

Hi, I've noticed that I've been getting the "Safari can't find the server" frequently for websites such as parse.com, Facebook and MacRumors too.

Another thing I'm suffering from is, each time I try to log into Facebook, I get to enter the username and the password. Even if I check the remember me option in Facebook login, still the next time I enter the Facebook.com url, my browser gets landed on the login page always. Sometimes I get re-directed to login page while I browse Facebook.

Could this be a malware problem? Any ideas?