Question about activation

There are two issues I can see...

If the old system came with the windows 7 installed it would likely be an OEM copy and thus not movable to new hardware - Changing a hard disk is acceptable with this licence but installing the old drive into the New system or copying the contents of the old drive over would be seen by the copy of windows as if it was working on a new motherboard and other components so would fail to activate.

The other issue is a more practical one, Windows relies on drivers for all its components, so you would need to have Windows 7 drivers for hardware that you now have, a lot of manufacturers only make hardware drivers for the latest Operating system, so the system would work with Windows 10, But not with Windows 7. the only way to get around this issue is if your new system was also available with Windows 7 and the drivers are still available (this is unlikely )

It should be, if you have a retail licence that is unlimited re-installs. The drivers may be more of an issue but sometimes you can get a driver for something like a network card or Bluetooth radio by going to the actual chip manufacturers for drivers that the full hardware makers do not make. More difficult are special functions, Normally laptops with "special" keyboard functions or lighting but other things can affect desktops, then again, most of these are not what I would call essentials

Before you start you should check you new processor for compatibility Intel had made a decision to not support some of their recent units on Windows 7 there are a few threads around the forums here that discuss options

One other thing I would do for the Windows 10 install is log in at least once with a Microsoft ID (you can even create one just for this purpose).

This will provide the fullest protection to the Windows 10 Licence should you need to ever reinstall it, the Association of the licence to a Microsoft Account even allows Windows 10 users to change the Motherboard and retain the licence.