Transferring Windows 7 to custom built desktop without OS

Recently, I decided to order the parts to a new gaming desktop, to replace my aging laptop. It's a HP Pavillion dv7, and either a 2xxx or 3xxx model, running Windows 7 Home Premium. I'm signed up to get Windows 10, but I'm willing to delay the upgrade until I get my problem sorted out.
My problem? I didn't order an OS for the gaming desktop as a cost cutting measure. Now I realize that as soon as the parts arrive, I'm going to be stuck with a nearly-useless piece of silicon and plastic or I'll have to use Ubuntu.

Thus, I am here to ask if it is possible for me to take the hard drive from the laptop, put it in the case of my new desktop, and have Windows run. Then I'd like to move Windows to the new 2TB hard drive I bought, and then delete the Windows on the laptop hard drive. (Yes, I already checked to see if my desktop case has places to mount

I have previously read this thread, but I have some concerns.
My concern is that my laptop came with Windows 7. Thus, I'm not sure if HP will let me re-activate my copy of Windows 7, leaving me back at square one. Secondly, that thread mentions that I won't be able to move an upgraded copy of Windows using that method. It mentions this referring to an upgrade from Vista, but I figure that this won't work if I upgrade to Windows 10 and try to transfer that over.
And here's a TL;DR version:
1. Can anyone here confirm that I would be able to move my copy of Windows 7 that came preinstalled on a HP Pavilion dv7 laptop to a desktop without an OS?
2. If I can accomplish #1, can you give me or point me towards step-by-step instructions?
3.Can you point me towards instructions on how to transfer Windows and everything else on the HDD onto a different HDD?

I appreciate this very much.

This might be outside the scope of the forums, but if I upgrade to Windows 7 on the laptop to Windows 10, would I be able to transfer that?

I'm actually somewhat familiar with Linux already, having installed Kubuntu on a chromebook. So I'll be fine with that or Mint for now.
Fortunately, I happen to be getting a computer science degree in a college that has a DreamSpark partnership with Microsoft. So I can get Windows Embedded Industry Pro in 7, 8 or 8.1 for free. Which, I've read, can be upgraded to Windows 10.