Learn Arabic (Modern Standard): قفز الممثل قفزة واحدة في هذه اللقطة.

Because قفزة is a Noun of Once. By taking the root letters of the verb قفز (to jump) and putting them into the فَعْلَة pattern, it specifically means a single instance of jumping, rather than the general concept of jumping.

Why does the sentence repeat the root, saying قفز الممثل قفزة (literally jumped the actor a jump)?

This structure is called the absolute object. In Arabic, you often follow a verb with a noun derived from the same root to emphasize the action or, as in this case, to specify exactly how many times the action happened.

Since the pattern of قفزة already means it happened once, isn't adding واحدة (one) redundant?

It is slightly redundant, but very natural in Arabic! While قفزة alone means a single jump, adding واحدة acts as an emphasizing adjective to stress that it was exactly one jump and no more.

The word اللقطة (the shot) seems to have the same فَعْلَة pattern. Is it also a Noun of Once?

Yes! It comes from the verb لقط (to capture or pick up). Originally meaning a single instance of capturing, it has become the standard everyday noun for a camera shot, take, or photograph.