Yes, there’s a few issues with running MRtrix3 that relate almost exclusively to our use of modern standards: the 2011 C++ standard (C++11), and OpenGL 3.3. Neither of these are actually all that new, but support for these in established stable distributions is often very outdated.
Of these, the OpenGL issue is the hardest to deal with (C++11 is typically just a matter of upgrading the compiler, or switching over to clang++). From what you say, it sounds like support for your GPU is still not stable enough for routine use - there’s no reason for Gnome3 to crash when using MRView unless there are bugs on their side. I’d be surprised if your WM crashes were really limited to using MRView, I’d expect any other GPU-intensive OpenGL application would also cause issues.
OpenGL support can however be tricky to get right - especially these dual GPU laptops (although I have to admit I’ve no direct experience with that). In my experience, getting stable OpenGL 3.3 support through the open-source mesa drivers (e.g. nouveau, radeon, etc) requires at least mesa 10.6, which only became available a year or so ago. Otherwise, it’s best to use the proprietary drivers (nvidia or fglrx for AMD/ATI), the tricky part there is installing them - it’s always going to be distribution-specific to some extent. That said, I’ve not had any major issues running the NVidia proprietary drivers for the last 3 years on my Arch Linux desktop (or for the last 15+ years that I’ve been using Linux). Work on the current version of MRView started back in ~2011, and was already relying on OpenGL 3.3 back then, so the NVidia proprietary drivers on Linux were good enough for that at the time. This was running Ubuntu 10.10 and eventually 12.04. Many users run Ubuntu 12.04, 14.04, or 16.04, and while getting the drivers installed can sometimes be tricky, for the most part people seem to manage fine (Ubuntu provides a simply utility to select open-source or proprietary drivers, which really helps).
So I’d recommend you try to install the nvidia proprietary drivers, rather than relying on the open-source ones. If you can’t get them working on Debian 8, consider using Ubuntu 16.04 instead (it’s a Debian derivative anyway). And if you like going commando, you can try Arch Linux (but be warned, it’s not the most user-friendly installation process).
As @rsmith says, running on Windows is fine, but for now it has to be through MSYS2 if you want GUI support. That’s because the WSL doesn’t include support for X11, and even if you do install a standalone X11 client, it won’t support OpenGL 3.3 (at least as far as I’m aware). With MSYS2 on the other hand, the software is compiled natively, and will access the native OpenGL environment directly. This works fine on my Win10 laptop, but as @rsmith says, you won’t get FSL that way (unless you manage to compile it within MSYS2 - no idea how hard that might be).
For the record, my setup is a 6-core i7-4930K CPU with 32GB RAM, equipped with a NVidia GeForce 780 GTX. It runs Arch Linux, Gnome Shell 3.22, using the NVidia proprietary drivers. As of a couple of months ago, it can also run on the open-source nouveau drivers, but there were a couple of minor issues at the time I tried (can’t remember exactly what they were, but nothing major). Given that this is a similar generation to yours, I’d expect support for it using the open-source nouveau driver is also not going to be stable for your card - it’s only just become sufficiently stable on my system, and Arch is one of the most up to date distributions out there. Debian focuses on stability, and so often ships with old software - I doubt your mesa installation is sufficiently current for this to work. Best to use the proprietary drivers in your case.
My previous laptop was a 2008 HP Pavillion dm3-1033tx, with a Core2 Duo CPU and a NVidia GeForce 105M GPU, also running Arch and Gnome3, this time using the open-source nouveau drivers (works fine on that generation of GPU), and using Wayland rather than Xorg. Everything worked fine there, although performance for the volume render was slow for full screen rendering (not altogether unexpected given how old that laptop is). But nothing like the kinds of issues you’re reporting here.
That laptop still works, but I’ve recently upgraded to a HP Spectre x360 with an intel GPU running Windows 10. MRtrix3 runs fine on MSYS2 on that system, and it also works fine out of the box on Linux (Arch Linux again).
Hope this helps.