Unless you have the expensive panel for the Linux version then you can't use Resolve in Linux as it will only work with the expensive panel.
QuickTime still works fine under Windows 10 just don't install the player or web plug-in components.
The latest version of Resolve shouldn't need QuickTime, although it depends on what's inside the .mov files as .mov is just a wrapper and can contain any number of different codecs inside.
Again, depending on what is in the files depends on how powerful a CPU you need. If they are h264 based then you will need a powerful CPU to decode the footage, especially if you want to decode multiple streams at the same time, then you will need powerful GPU's for the real-time playback, so if possible 2 GTX 1080's would be good