Wanneer Tom verdrietig is, probeert Anna hem te troosten.

Because Wanneer Tom verdrietig is is a subordinate clause. In Dutch, the conjugated verb often goes to the end of a subordinate clause.

So:

• Wanneer Tom verdrietig is
• literally: When Tom sad is

This is normal Dutch word order.

Compare:

• Tom is verdrietig. = main clause
• Wanneer Tom verdrietig is... = subordinate clause

In the main clause, is comes earlier. In the subordinate clause, it moves to the end.

This is because Dutch main clauses follow the verb-second rule.

When the sentence begins with the subordinate clause Wanneer Tom verdrietig is, that whole clause takes the first position. Then the finite verb of the main clause must come next.

So the structure is:

• Wanneer Tom verdrietig is, = first position
• probeert = finite verb in second position
• Anna = subject
• hem te troosten = rest of the sentence

That is why Dutch says:

• Wanneer Tom verdrietig is, probeert Anna hem te troosten.

and not:

• Wanneer Tom verdrietig is, Anna probeert hem te troosten.

Yes. Verdrietig is an adjective, meaning sad.

In this sentence it is used predicatively, after the verb zijn (to be):

• Tom is verdrietig. = Tom is sad.

When an adjective is used this way in Dutch, it does not take an extra ending like -e.

So:

• de verdrietige jongen = the sad boy → adjective before a noun
• de jongen is verdrietig = the boy is sad → adjective after is

Hem means him and refers to Tom.

In the sentence:

• probeert Anna hem te troosten

Anna is trying to comfort Tom, so Dutch uses the object pronoun hem.

A quick comparison:

• hij = he → subject form
• hem = him → object form

So:

• Hij is verdrietig. = He is sad.
• Anna troost hem. = Anna comforts him.

After proberen (to try), Dutch normally uses te + infinitive.

So:

• proberen te troosten = to try to comfort

This works a lot like English to try to do something.

Examples:

• Ik probeer te slapen. = I’m trying to sleep.
• Zij probeert hem te helpen. = She is trying to help him.

So in your sentence:

• probeert Anna hem te troosten
• literally: Anna tries him to comfort
• natural English: Anna tries to comfort him

Because hem is the object of troosten, and in Dutch object pronouns often come before the infinitive.

So Dutch says:

• Anna probeert hem te troosten.

rather than something shaped like English word order.

A useful way to see it is:

• probeert = finite verb
• hem = object pronoun
• te troosten = infinitive phrase

This order is very normal in Dutch.

Yes, often you can.

Both can mean when in sentences like this, but there is a slight difference in feeling:

• wanneer often sounds a bit more like when / whenever
• als is very commonly used for if and also often for when in everyday Dutch

So these can both work:

• Wanneer Tom verdrietig is, probeert Anna hem te troosten.
• Als Tom verdrietig is, probeert Anna hem te troosten.

In many everyday situations, als is more common in speech, but wanneer is absolutely correct and clear.

Because the sentence begins with a subordinate clause, and Dutch normally separates that clause from the main clause with a comma.

So:

• Wanneer Tom verdrietig is, probeert Anna hem te troosten.

The comma helps show where the first clause ends and the main clause begins.

This is very common in Dutch when a dependent clause comes first.

Yes.

You can say:

• Anna probeert hem te troosten wanneer Tom verdrietig is.

This means the same thing.

Notice the difference in word order:

• If the sentence starts with the subordinate clause, you get inversion:
  Wanneer Tom verdrietig is, probeert Anna...
• If the sentence starts with the main clause, you keep normal main clause order:
  Anna probeert...

Both are correct.

Because that would mean Anna comforts him, not Anna tries to comfort him.

Your sentence includes the idea of trying, so Dutch uses:

• probeert ... te troosten

Compare:

• Anna troost hem. = Anna comforts him.
• Anna probeert hem te troosten. = Anna tries to comfort him.

So proberen adds an important meaning.

No, not in this form.

It is a subordinate clause, so it needs a main clause to complete the thought.

• Wanneer Tom verdrietig is... = When Tom is sad...

An English speaker can feel that something is still missing, and the same is true in Dutch. You expect the rest of the sentence:

• Wanneer Tom verdrietig is, probeert Anna hem te troosten.

By contrast, this is a complete sentence:

• Tom is verdrietig. = Tom is sad.