Can anyone tell me from where I can see my previous games that were played months ago? In the games archive, I can see games that are only a weeks old. Rest of the games are nowhere to be seen. 

Chess.com only keeps a record of past games for longer than a month for paying members. If you wish to mantain a record of your past games you will have to download the pgn files and archive them yourself (or cough up the cash for a membership )

Actually Chess.com keeps all their games in the archive, but getting access to it is a premium feature. So if you buy membership, you will have access to all games you have played so far.

Well, one thing is for for sure that they do have the record for my past games because I had the pgn file of one of my old games. And when I redownloaded that file, it was successfully downloaded. It shows that the pgn's old games of even the free members are there to download.