Hi again,
The secondary WD Blue is a great drive for storing data.
You won't have any problem disconnecting the WD Blue from your sick computer, and attaching it to the temporary machine. Once you do that, Boot up to the desktop, Rt Clk on My Computer, and click "Manage", then on Disk Management. Look in the graphical area toward the bottom, and you will see the WD Blue attached. There are two sections to review. On the left end of the WD Disk, is the Disk Status Info. If should read Disk # 1,2,or 3 depending on how many other HDD's are attached. Then is should say "Basic", then the size in GB, and "Online". Then in the middle Volume Status section there should be a dark Blue band across the top, and it should list the Drive friendly name, or Drive E: (or similar), any Partitions on the Disk, size of each and most importantly "Healthy". Don't change anything here, just review the info. If any different than listed above, let us know. If it is as above, you are OK to go ahead and use it from File Explorer, or with Apps without any problems.
Regarding your second question, depending if the computer is an OEM model, you may well have to call MS to reactivate the OS if the MB has changed or they send you a new replacement rather than replacing a bad component..
That can be tricky, and frustrating if Win-10 is the OS and the UEFI Secure Boot is on, as is the default.