@ranochigo: Thanks for the response. So, I can continue using Bitcoin Core version: 0.13.1.0 without any issues right or should I upgrade my Bitcoin Core version?
It's definitely recommended to upgrade, not due to the fork but due to the general improvements over the version.
Also, how can I get the Bitcoin Cash coins since I do own my private keys (the wallet)?
You can either import it into Electron Cash or just install the Bitcoin Cash client and use it from there. Just to say, there is obviously risks associated with running and/or importing private keys into a foreign client. You have to check to make sure that you get the client from the legitimate source and can verify it.
1. Go to %appdata% or your data directory.
2. Copy out your entire Bitcoin folder into another location.
3. Download Bitcoin Cash and point the data directory at the folder you've copied out.
Close the other thread if possible.