I currently own a Redmi Pro running Android Marshmallow with MiUi 8. Is it possible to install Android 7 Nougut on my phone.. I already have root...
Not stock, you would have to install a custom ROM that is specifically designed for your device, they are not generic... Check XDA here: https://forum.xda-developers.com/redmi-pro in the Xiaomi Redmi Pro ROMs, Kernels, Recoveries, & Other Development section. Make sure to do your research and understand the implications and process of installing a custom ROM before starting. Reading in the various XDA forums under your device is a good place to start.
In looking in the development area for your device, it seems the only Nougat ROM in active development is LineageOS 14.1, which is still in alpha stages since some things are not working, major things like calls, camera, mobile data, and more, some major hurdles to overcome yet.
So to answer your question regarding your device, yes, you can but you will not have a fully functional device at this time. I would monitor those areas and see if development continues otherwise it appears you are stuck on Marshmallow.
To answer your generic question, "Can I Install Stock Android 7 N On Any Device?", no you cannot... Android ROM's must be built specifically for each device, they are not generic and not even the same for very closely related devices in almost every case. Some devices have Nougat support from their manufacturer, some have it from third party ROMs, and many do not and will never have it.