Using an open source software may be a good start to improving democracy and creating the principles for such. Spreading the word and making suggestions and showing people how to be democratic is a good thing and shows them that peace matters and the world still has a chance at being peaceful.
Yes, governments should use open source software, because it would allow people more access to information, because other people would be able to use the code in order to help others. Other people would create derivative websites and self-help websites, which would increase the public's ability to understand government processes and services. Open-source is also fair, because the public pays taxes, and should be able to use what is produced with their tax money.