Co-incidentally whilst I do not have PhotoStory, I do have Movie Edit Pro and it was a question that I was wondering about a month ago. If though you are running Windows 10 you may have the solution, for free, already installed.
As part of the Windows set up you may already have the Xbox app installed. Windows G brings the record screen keyboard up. Checkout this video I found on youtube that helped me.
No, PS does not include any capability to record your screen. Magix Movie Edit Pro and Video Pro X both support this feature but the general consensus amongst users is that it is best to use a dedicated program for this. Do a Google search for "screen recording software" and you will see there are a large number, both free and paid-for. A popular free one is OBS but users who attempt to edit the footage with Movie Edit Pro or Video Pro X have generally not enjoyed a happy experience.
Theoretically, you could edit the footage n PS but this is not advised since the video facilities within PS are not at all extensive.