Can I restore an iPhone from a previous version of iOS?

I will be getting a iPhone X, but my iPhone 7 Plus is still on iOS 10 due to the fact of issues with iOS 11 on some devices and I'm just playing it safe. When I get my iPhone X, will it be able to use my current back up on iTunes with the file coming from iOS 10, or do I need to update my iPhone 7 to iOS 11 for it to be compatible?

No, but the iPhone x will have the new iOS 11.1 with bug fixes

If your iTunes version is iTunes 12.7, then you need to update to iOS 11, or your device can't be recognised by iTunes.
If you just want to restore your iPhone, or transfer files from your iPhone 7 to new iPhone X, then you can have another better choice to complete the job. This way is different from iTunes, it will not erase data and settings on your device. And it has helped plenty of iOS users successfully transfer files from iPhone/iPad/ to iPhone/iPad/Mac/PC. Just 1 click and a few minutes are needed.

I don't see why not, but of course it wouldn't be running that version of iOS at the end of the day. Basically your data would be on iOS 11.1