1. You need an older video card with an NVIDIA graphics chipset or Intel
graphics. Not all games for GNU/Linux will work although many of the older
titles will. The 9500GT is a good choice for graphics.
http://libre.thinkpenguin.com/ - 25% of the profits from sales go to
Trisquel. Everything here is free software and will work with Trisquel 99%
works out of the box (and 100% with a little effort, the rest of stuff will
work tomorrow out of the box, such hardware is noted on the product pages)
2. You shouldn't have any problems mining Bitcoins although CPU mining isn't
a realistic option any more. Using a graphics card is not an option although
this won't be an option for anybody very shortly either anyway. ASIC hardware
is the future (actually it is here already) of bitcoin mining.
3. There is Cinelerra for video editing although chances are you probably
aren't actually a profesional and what you want is something comparable to
whats available for MS Windows / Apple. For that I'd point you to OpenShot.
There are others although this one is easy enough to use and works really
well. It may be a bit weak on the features compared to other consumer video
editing applications. There are other video editing applications for
GNU/Linux that are free which may have a bigger feature set. They may or may
not work as well. Cinelerra is more for large development houses looking to
produce hollywood length films than your one man show or small team. It has a
steep learning curve although is extremely powerful. It supports things like
distributed encoding so you can have hundreds or thousands of systems working
together to produce your video. You would also probably have to use a
distribution which includes non-free software simply because the software
itself is so complex and tailored for Redhat Enterprise GNU/Linux or maybe it
is SuSE (I believe they distribute RPMs and I don't think there are any DEBs
for Debian/Ubuntu).