Hey OP,
http://www.blender.org/
Blender is meant to be the best or one of the best open source editing software.
It looks a bit intimidating but apparently is easy to learn the basics.
If you look at the features page you can see it has video editing.
I've just downloaded it and will start using it shortly.
For game capture try
https://obsproject.com/
It uses flash to capture the game and the recorded footage is a little flat compared to commercial products but its so lite on your system requirements there is not much fps drop.
And it can stream very well to twitch if you have the connection to do so.
These are Open Source so are considered safe and have no trial or paid for upgrade options.
There is no T+C's that stops you from using these commercialy either.