Why would a new MacBook Pro charger fail in one month?
What might be happening?


You have a defective charger.  It's not unheard of and if you are a manufacturer of products, it's quite common.  With every single product that is made around the world, there is a percentage that fail.  This is called a defect percentage or rate.


  The total number of defects counted on the population in question
  divided by the total population count.


At one point, Apple was expecting a 10% defect rate on iPhones made by Foxconn.1

Does this mean that they are just going to let defects go?  Of course not, but being that these are complex products dependent on the manufacturing processes of other vendors, defects are bound to show up.  Even with the best QA processes in place, it's not perfect.

You received a charger that failed.  This is why they offer you a warranty.

As for the electric feeling, this also is a common occurrence and has been discussed on this site:


How can I avoid my MacBook Pro giving me minor shocks?
Is it bad that my MacBook Air is passing me electricity?
Avoiding electrical shocks/statics


Basically, it boils down to the adapter not being grounded/earthed and using a 3 prong plug (applicable to your country) solves the problem.  



1 Apple Expected 10% Bad iPhones from Foxconn?  Mark Graban's Lean Blog, May 6, 2013.