Battery Cycles being used very fast
I am using a 13-inch mid 2014 MacBook Pro with Retina Display. It is
  about 3 weeks old and already has clocked 13 charge cycles. Is this
  too high?


A charge cycle is just the process of using and then recharging the full capacity of the battery one time. From Apple:


  A charge cycle means using all of the battery’s power, but that
  doesn’t necessarily mean a single charge. For instance, you could use
  your notebook for an hour or more one day, using half its charge, and
  then recharge it fully. If you did the same thing the next day, it
  would count as one charge cycle, not two, so it may take several days
  to complete a cycle.


You can't really have "too many" charge cycles unless there's something wrong with the battery and it's unable to hold a charge. That seems unlikely since your computer is brand new (and OS X will notify you if your battery condition is abnormal).

Furthermore, your particular model is rated for 1,000 charge cycles before it's considered "consumed" (meaning it'll no longer hold a reasonable charge and will likely need to be replaced). If your current rate of 13 charge cycles per three weeks holds, that means you're good for 4.5 years – in other words, nothing to worry about!


  Also, I follow the practice of fully charging it and then using till
  about 40% before recharging without ever leaving it plugged in. Is
  this the best practice to follow or should I leave it plugged in while
  charging ?


Even if you leave your laptop plugged in at 100%, the system will actually silently discharge the battery to ~95% and back up to keep things moving. Apple used to recommend unplugging your laptop at least once a month, but their current guidelines make no mention of that, so I wouldn't worry about it.