Wir bearbeiten das unscharfe Bild vorsichtig nach.

Because the full verb here is nachbearbeiten, which is a separable verb.

In a normal main clause in the present tense, German splits separable verbs into:

• the conjugated main part in position 2: bearbeiten
• the prefix at the end: nach

So:

• Wir bearbeiten das unscharfe Bild vorsichtig nach.

This works like:

• Ich stehe früh auf. = I get up early.
• Sie kauft im Supermarkt ein. = She shops at the supermarket.

In an infinitive or participle, the verb stays together:

• das Bild nachbearbeiten
• Wir wollen das Bild nachbearbeiten.

Nachbearbeiten means something like:

• to edit afterward
• to retouch
• to post-process
• to touch up

It suggests that the image already exists and is being improved or corrected afterward.

So this is not just to work on an image in a general sense. It specifically has the idea of further editing or editing after the initial creation/capture.

Because Bild is neuter and here it is in the accusative case as the direct object.

After the definite article das, the adjective takes the weak ending -e in nominative or accusative singular neuter.

So:

• das unscharfe Bild = the blurry image

Compare:

• ein unscharfes Bild = a blurry image

Why the difference?

• After das, the article already shows the gender/case clearly, so the adjective ending is weaker: -e
• After ein, the article gives less information, so the adjective ending has to carry more: -es

It is the direct object of the verb.

The subject is:

• Wir = we

What are we editing?

• das unscharfe Bild

That makes it the thing receiving the action, so it is in the accusative.

Because Bild is neuter, the definite article is:

• nominative: das Bild
• accusative: das Bild

So the article looks the same in both cases, but grammatically it is accusative here because it is the object.

Unscharf usually means:

• blurry
• out of focus
• not sharp

For an image, this is the natural meaning.

Be careful not to translate it too mechanically as English unsharp, because in normal English blurry or out of focus is much more natural.

Here, vorsichtig is being used as an adverb, not as an adjective directly before a noun.

It describes how the action is done:

• vorsichtig nachbearbeiten = to edit carefully

In German, adverbs often have the same form as the adjective:

• ein vorsichtiges Kind = a careful child
• Das Kind handelt vorsichtig. = The child acts carefully.

So unlike English, German usually does not add a special ending like -ly.

The most important fixed rule is that in a main clause:

• the conjugated verb must be in second position
• the separable prefix goes to the end

So this pattern must stay:

• Wir bearbeiten ... nach.

But the middle part can sometimes move around.

For example:

• Wir bearbeiten das unscharfe Bild vorsichtig nach.
• Wir bearbeiten vorsichtig das unscharfe Bild nach.

Both are possible, though the first version sounds very natural and neutral.

German word order in the middle of the sentence is somewhat flexible, but it is not random. Changes in order can affect:

• emphasis
• rhythm
• what sounds most natural in context

No, not in a normal main clause.

That would be wrong because separable verbs do not stay together when conjugated in a main clause.

Correct:

• Wir bearbeiten das unscharfe Bild vorsichtig nach.

You only keep nachbearbeiten together when it is:

• an infinitive: Wir wollen das Bild nachbearbeiten.
• a participle: Wir haben das Bild nachbearbeitet.

Yes. German is a verb-second language, which means the conjugated verb must be the second element, but the first element can vary.

So you could say:

• Wir bearbeiten das unscharfe Bild vorsichtig nach.
• Das unscharfe Bild bearbeiten wir vorsichtig nach.
• Vorsichtig bearbeiten wir das unscharfe Bild nach.

All of these are grammatically possible, but they place emphasis on different parts.

The version with Wir first is the most neutral if you are simply stating what we do.

Both are possible, but they mean slightly different things.

• bearbeiten = to work on, edit, process
• nachbearbeiten = to edit afterward, retouch, post-process

So:

• Wir bearbeiten das Bild.
  = We edit/process the image.

• Wir bearbeiten das Bild nach.
  = We retouch/post-process the image.

The version with nach adds the idea of further editing after an earlier stage.

You learn it as part of the noun:

• das Bild

In German, it is very important to memorize nouns together with their article:

• der
• die
• das

That helps you form correct case endings and adjective endings later.

Here, knowing it is das Bild helps explain:

• das unscharfe Bild
• not der or die Bild

It also helps with plural forms:

• das Bild
• die Bilder