Unser Hund will von allen Kindern gestreichelt werden.

Because Hund is the subject of the sentence, so it must be in the nominative case.

• der Hund = the dog
• unser Hund = our dog

If it were a direct object, you would use the accusative:

• Ich sehe unseren Hund. = I see our dog.

Here, our dog is the one that wants something, so it is nominative: unser Hund.

No. In modern German, will is usually the form of wollen, meaning to want.

So:

• Unser Hund will ... = Our dog wants ...

It does not normally mean the English future will.

Forms of wollen:

• ich will
• du willst
• er/sie/es will
• wir wollen
• ihr wollt
• sie/Sie wollen

This is because the sentence uses a passive infinitive after the modal verb will.

The basic idea is:

• streicheln = to pet / to stroke
• gestreichelt werden = to be petted / to be stroked

So the structure is:

• will
  • passive infinitive

That gives:

• Unser Hund will von allen Kindern gestreichelt werden.
• literally: Our dog wants by all children petted to be
• natural English: Our dog wants to be petted by all the children.

Because after a modal verb like wollen, German puts the dependent verb phrase at the end, and in a passive infinitive the order is:

• past participle + werden

So:

• gestreichelt werden = to be petted

This same pattern appears in other examples:

• Der Brief muss geschrieben werden. = The letter must be written.
• Das Auto kann repariert werden. = The car can be repaired.

So gestreichelt werden is the normal infinitive passive order.

In a passive sentence, the person or group doing the action is often introduced with von.

Here:

• von = by
• von allen Kindern = by all the children

So the sentence says that the dog wants the action to be done by all the children.

This is a standard passive pattern:

• Das Buch wird von der Lehrerin gelesen. = The book is read by the teacher.
• Der Hund wird von den Kindern gestreichelt. = The dog is petted by the children.

Because von always takes the dative case.

The base phrase is:

• alle Kinder = all children

But after von, it becomes dative plural:

• von allen Kindern

So:

• alle Kinder = nominative/accusative plural
• allen Kindern = dative plural

You can think of it as:

• by all the children → von allen Kindern

Gestreichelt is the past participle of streicheln.

• streicheln = to stroke / to pet
• gestreichelt = stroked / petted

German uses the past participle in several structures, including the passive:

• Der Hund wird gestreichelt. = The dog is being petted.
• Der Hund will gestreichelt werden. = The dog wants to be petted.

So in this sentence, gestreichelt is not acting like a normal adjective by itself; it is part of the passive verb phrase gestreichelt werden.

Yes. An active version would make the children the subject:

• Alle Kinder wollen unseren Hund streicheln.
• All the children want to pet our dog.

But that does not mean exactly the same thing in focus.

Compare:

• Unser Hund will von allen Kindern gestreichelt werden.
  • focus on the dog and what the dog wants
• Alle Kinder wollen unseren Hund streicheln.
  • focus on the children and what they want

So the passive is used here because the sentence is centered on our dog.

Usually, von is used for the agent of a passive action, especially when it is a person or living being.

• von allen Kindern = by all the children

Durch is more often used when the action happens through some means, process, or cause rather than a personal agent.

Compare:

• Der Hund wird von den Kindern gestreichelt. = The dog is petted by the children.
• Der Hund wurde durch ein Geräusch geweckt. = The dog was awakened by a noise.

So in this sentence, von is the natural choice because children are the ones doing the action.

German main clauses usually have the conjugated verb in second position.

So the structure is:

1. Unser Hund = topic/subject
2. will = conjugated verb
3. everything else
4. the remaining verb elements at the end

That gives:

• Unser Hund | will | von allen Kindern | gestreichelt werden

This is very typical for German:

• Der Mann will morgen nach Berlin fahren.
• Meine Schwester kann gut Klavier spielen.
• Unser Hund will von allen Kindern gestreichelt werden.

Yes. Grammatically, that is correct.

• will = wants
• möchte = would like

Möchte often sounds softer or more polite in human speech. With a dog, both are understandable, but will sounds more direct and stronger, which often fits an animal’s desire quite well.

So:

• Unser Hund will ... = Our dog wants ...
• Unser Hund möchte ... = Our dog would like ...

Both work, but they are slightly different in tone.