I've been running A:M on a laptop with Windows 8 and haven't had any issues.
To transfer the license to the new computer, contact Jason.
As far as recommended specs, someone else may know. I consider what I'm currently using as underpowered for some things, mostly because it doesn't have a dedicated graphics card, but it can do quite a bit for what it is...it has a middle-of-the-road i5 and 6GB of RAM. Of course, the speed of the processor, the amount memory, the amount of video memory, having a dedicated video card and type of hard drive will affect how good your experience will be. What I think would do the job for me, would be an i7 4800MQ processor, 16GB of RAM, at least 2GB of video RAM (more would be better), 1920x1080 anti-glare display with an SSD hard drive...but you can get by with less.
Hope that helps.