Is it possible to install windows 7 onto a hard drive connected to a computer via a dock, if so how?

No it's not possible.

When Windows 7 is installed like any version of Windows post 2000, a Hash is created based on the hardware components, motherboard etc. This Hash is checked every time the computer is booted and if there is any major hardware change that causes the new hash to mismatch the old one, then Windows will trigger its anti-piracy functions and prevent the OS being run without first reactivating. Failure to reactivate will cause Windows to 'brick' itself and become unusable.

Windows 7 needs to be installed on one hard drive attached to one computer and cannot be moved to another without the anti-piracy controls kicking in.

Edit: The drive itself is still usable. You can remove it and place it in another PC you just can't use the Windows install that's on the drive. You can wipe it and use the drive like new, or if you want to keep the data that's on it then you can just start a new Windows Installation, setup will detect any existing Windows Install and move it into an archive folder and should leave the rest of the data untouched.

No to the first question and while not impossible its more luck than anything else, to the additional question.

I have done this in the past and been lucky but invariably you will have driver conflicts from the motherboard, Windows will likely see the new system as a new PC and require reactivation. But I would say percentage wise you'll have a 10 - 20% chance of success moving a HDD to another system, not good odds.

You could install Windows 7 to a virtual HDD using a virtualisation program like VirtualBox, VirtualPC or VMware, the first two are free.

Yes