I've been using BSD for a long time, both in OpenBSD and FreeBSD. FreeBSD is fantastic. I use mostly just plain Xorg and i3 window manager. With emacs, LaTeX and conkeror I can accomplish all that I need to do, and do it efficiently. However you can put as many bells and whistles on your installation as you want. True, you could do that with linux but there are some very important advantages with using FreeBSD:
1/ ZFS file system. This alone is worth switching to FreeBSD. If you don't know what it is, learn how to use it. What is extremely useful is doing "zfs send" of snapshots to another machine. Need more storage? Just add a disk to the pool. ZFS is very much production grade in FreeBSD 10.1.
2/ Jails. These are better than VirtualBox in my humble opinion, but they do have a learning curve. The advantage is putting each jail on a zfs filesystem where you can do snapshots of different stages of your application deployment and if something doesn't work you can simply rollback. Yes, I know you can do this with VMWare and the rest but jails allow me to access the filesystem directly in the command line and in general it is much more intuitive for my work habits. Note that you can also install jails of different flavors - for instance a debian jail where you can run everything just like it is on linux.
VirtualBox works just fine on FreeBSD, but I'll admit I haven't used it much.
3/ General simplicity of the system. Linux is fastly becoming as non-unix like as possible [though to be fair GNU is Not Unix]. Just a simple install of Ubuntu and you will see tons of processes running that you sometimes wonder what they are all up to. This may provide some utility for some people, but most people will never use those features. In FreeBSD I know exactly what each process is doing and it is very easy to turn off or enable as I desire. FreeBSD provides me control because I know the system, and the system is easier to know because it is much simpler and in my opinion more coherently designed.
4/ Much better documentation. FreeBSD (and BSD in general) has a good reputation for providing documentation. Almost everything you need is in the handbook. Also there is a lot of stability in the way things are done. Often in Linux the entire manner of doing things is changed from one version to another. Plus there are no monstrosities like NetworkManager which are opaque and not very well documented.
5/ More secure - a system is only as secure in as much as you know how it is working and what it is doing. In this case FreeBSD is more secure because I know more of what it is doing. With Ubuntu giving web searches every time you try to find a file on your machine, there is just asking for trouble.
6/ The system is more responsive. FreeBSD simple feels more 'alive' in the sense it is doing only what you want it to do. You don't have to wait for that useless application to stop doing what it is doing because it is not there. You don't need to wait for the indexing of the harddrive to give you back control of the system, as you decide when it should be done, etc. But I think even the UI elements are much smoother even on large desktops like KDE. The scrolling of windows for instance seems much more responsive than it is on linux, but that could be due to all sorts of factors.
As to your particular needs:
A/ Minecraft works just fine. http://minecraft.gamepedia.com...
B/ I have no idea, but an acquaintance tells me it works. In the forums they mention FreeBSD so someone must be using it.
C/ Mplayer works just fine, but I've seen a lot of people use VLC.
D/ Firefox works extremely well, though I use Conkeror which is simply a different shell to the same browser.
E/ Flash works with a multiple of different options.
F/ No idea to be honest about OpenRA. If there is source code I'm sure you could get it to run. At the very worst there is a linux-emulation layer.
G/ All the major Desktop Environments are in the ports tree. KDE, Mate, Gnome, Openbox and XCFE can also be installed with precompiled packages.
H/ Not an expert on this, but you can check out the handbook, as it seems to say yes: https://www.freebsd.org/doc/ha...
I/ Qt is in the ports tree.
Literally, you can do with FreeBSD whatever you want. If you want to experiment, perhaps try some of the various guides:
If you want to just stick in a DVD and have it all done for you, I would suggest going with PC-BSD: http://www.pc-bsd.org/
Good luck to you !