I think the cable of the second image will not be useful in Intel Galileo Gen 2.
There are several threads about RS232 communication/s in Galileo Gen 2:
This message was posted on behalf of Intel Corporation
As Fernando mentioned the 3.5mm cable won't help you when using a Gen 2. I'd suggest you to check the following document in order to learn which cable you should use with each Galileo: http://www.intel.com/content/www/us/en/support/boards-and-kits/intel-galileo-boards/000006343.html
Also, you mention that you would like to use C#, may I ask which image you are using? If you would like to use C# you will have to install mono's packages from source, you'll find more information in http://www.mono-project.com/docs/about-mono/supported-platforms/linux/.
I hope this helps.