Для этого кадра изменили фокус.

Because the preposition для requires the genitive case.

• этот кадр = nominative, this frame/shot
• для этого кадра = genitive, for this frame/shot

Both words change:

• этот → этого
• кадр → кадра

So для этого кадра means for this shot/frame.

Кадр can mean frame or shot, depending on context.

Common uses:

• in film/video: shot
• in photography: frame or picture
• sometimes literally a single frame of film/video

So in this sentence, it most likely means something like this shot or this frame, depending on the translation you were given.

This is a very common Russian pattern. Russian often uses the 3rd person plural past tense with no subject to mean someone/they in a vague, unspecified way.

So:

• изменили фокус = they changed the focus
• but it often really means the focus was changed or someone changed the focus

It does not necessarily mean a specific group of people. It is an indefinite-personal construction.

English often uses:

• they changed...
• someone changed...
• or a passive like ...was changed

Russian often just uses the plural verb with no subject.

Because изменили is perfective. It presents the action as completed: the focus was changed.

• изменили = changed, made a change
• меняли = were changing / changed repeatedly / used to change

In this sentence, the speaker is talking about a finished action connected with that particular shot, so изменили is the natural choice.

Фокус is in the accusative case because it is the direct object of изменили.

They changed what?
→ фокус

Since фокус is a masculine inanimate noun, its accusative singular looks the same as the nominative singular:

• nominative: фокус
• accusative: фокус

So the form does not change, even though the case function does.

This is mostly about word order and emphasis.

Russian word order is flexible. Starting with Для этого кадра sets the context first:

• For this shot/frame, they changed the focus.

This makes this particular shot the topic.

A more neutral order could be:

• Фокус изменили для этого кадра.
• Изменили фокус для этого кадра.

All of these are possible, but the original sentence highlights for this shot first.

Yes. Для этого кадра means something like:

• for this shot
• for the purposes of this shot
• to suit this shot

It tells you that the change in focus was made with this frame/shot in mind.

This is different from:

• в этом кадре = in this frame/shot
• на этом кадре = on this frame/picture

So для этого кадра is not describing location; it is describing purpose/relevance.

Yes, very naturally.

Although the Russian sentence literally uses an active plural verb with no subject, English often prefers a passive translation:

• The focus was changed for this shot.

That is often smoother than:

• They changed the focus for this shot.

Both are possible, and both match the Russian meaning.

Here, yes, it is basically the same idea: focus in an optical or camera sense.

In Russian, фокус can also mean other things in other contexts, for example:

• a trick or magic trick
• a scientific focus/focal point
• a point of concentration

But in a film/photo sentence with кадр, it almost certainly means the camera/visual focus.

Yes, that is a possible natural English translation, depending on context.

Literally, the Russian says they changed the focus. In context, that may be expressed in English as:

• They changed the focus for this shot.
• They adjusted the focus for this shot.
• They refocused for this shot.

The exact best translation depends on whether the context is technical, cinematic, or more general.