Yes, you can participate in challenges with other FitBit users/friends and you can get badges using the Blaze. Challenges are only seen when logged onto the FitBit app, but badges can be seen on the FitBit app or if you log on to your account online. You cannot see progress of the challenges or what badges you have just by looking at your Blaze though.
Just like what @gpsoph said challenges are through the Fitbit app and can be done by anyone who has any kind of Fitbit. No specific models needed. Badges and challenges can't be seen from the Blaze itself though.