Billedet beviser, at han var der.

Billedet means the picture or the image.

The base noun is et billede = a picture / an image.
Danish often makes nouns definite by adding the article to the end of the word:

• et billede = a picture
• billedet = the picture

So the -et here is the definite ending for a neuter noun.

In Danish, when a noun stands by itself, you usually do not use a separate word for the. Instead, you attach the definite article as an ending:

• et billede = a picture
• billedet = the picture

So et billedet is incorrect.

A separate definite word like det is used mainly when there is an adjective:

• billedet = the picture
• det gamle billede = the old picture

Beviser means proves.

The infinitive is at bevise = to prove.

Examples:

• Jeg kan bevise det. = I can prove it.
• Billedet beviser det. = The picture proves it.

In this sentence, beviser is the present tense form.

Because at han var der is a subordinate clause: that he was there.

Danish normally uses a comma before subordinate clauses, especially in standard written Danish:

• Billedet beviser, at han var der.

That comma is very natural and expected in writing.

No. Here at means that, not the English preposition at.

So:

• at han var der = that he was there

This is a very common source of confusion for English speakers, because the Danish word at often introduces a clause, while English at usually shows place or time.

Also note that Danish at can appear before infinitives too:

• at være = to be

So at has more than one job in Danish.

In this sentence, der means there.

So:

• han = he
• var = was
• der = there

Together: han var der = he was there

Compare:

• her = here
• der = there

So:

• Han er her. = He is here.
• Han er der. = He is there.

Because the clause says that he was there.

Var is the past tense of er / være:

• at være = to be
• er = is / am / are
• var = was / were

So:

• han er der = he is there
• han var der = he was there

The sentence is talking about his presence at some earlier time, and the picture is being used as proof of that.

Great question. Danish does usually follow verb-second word order in main clauses, but not in subordinate clauses.

Main clause:

• Han var der. = He was there.

Subordinate clause after at:

• ... at han var der. = ... that he was there.

So after at, the normal order is subject + verb:

• han = subject
• var = verb
• der = adverb

You do not move the verb to second position in the same way as in a main clause opening with another element.

Yes, possibly.

Et billede can mean:

• picture
• image
• photo

The best English translation depends on context. If you are talking about a photograph as evidence, photo may sound more natural in English. If the context is broader, picture or image is safer.

So all of these could work depending on context:

• The picture proves that he was there.
• The photo proves that he was there.
• The image proves that he was there.

Usually bevise means prove, so it suggests fairly strong evidence.

• Billedet beviser, at han var der.
  = The picture proves that he was there.

If you want a weaker idea, Danish often uses verbs like:

• viser = shows
• tyder på = indicates / suggests

Compare:

• Billedet viser, at han var der. = The picture shows that he was there.
• Billedet tyder på, at han var der. = The picture suggests that he was there.

So beviser is the strongest of these.

Yes. Der can have several uses in Danish, which can confuse learners.

In this sentence, it clearly means there:

• han var der = he was there

But der can also appear in other patterns, for example:

• Der er en bog på bordet. = There is a book on the table.

In that kind of sentence, der is not really a location word in the same way; it works more like the English introductory there in there is.

So when you see der, always check the structure of the whole sentence.

Then you would use the present tense of være:

• Billedet beviser, at han er der.

Compare:

• han er der = he is there
• han var der = he was there

So the only change is:

• var → er

Yes. It is completely natural and grammatically standard.

It has a very typical structure:

• Billedet = subject
• beviser = main verb
• at han var der = subordinate clause

So it is a good example of:

1. a noun in the definite form,
2. a present-tense main verb,
3. a subordinate clause introduced by at,
4. past tense inside the subordinate clause.