I am building a Gnu/Linux distribution. I am keeping the kernel open source but the desktop environment and the programs (the ones built by me) on top of it will be proprietary. Is it possible? The GNU GPL v2 states that one cannot make the derivatives of GPL-licensed software closed source. Therefore I am not modifying the Linux kernel but adding some add-ons. And will there be any licensing problems if the project as a whole is to be closed source?
First of all, a GNU/Linux distribution consists of many software packages, some of which are licensed under GNU GPL, but there are other licenses involved as well. For example, Perl is covered under the Artistic License or GPL — your choice, and Apache is covered by the Apache license. That said, the GPL is one of the strongest copyleft licenses that you'll have to work with.
The GNU GPL only covers distribution; you don't even have to abide by its terms as long as you don't share your Linux distribution with anyone. If you do share it, though, anyone who receives a copy has a right to demand that you provide the source code. Alternatively, you could take an approach similar to Red Hat, which is to publish only the source code, but provide compiled binaries only to paying customers.
If you want to build a closed-source product, though, GNU/Linux is a poor base to start from. You could consider customize a system based on BSD instead.
The fun (I guess) would start at when you are giving support to people. If you are coding yourself all the proprietary packages/programs then you may be able to figure out most of the issues, if however, the proprietary softwares would be a different vendor, you may find yourself in a bigger mess in support. As has been shared, it would be good to get yourself a professional copyright lawyer