Quando ci salutiamo, il cane scodinzola.

Because ci adds the idea of each other.

• salutiamo = we greet / we say hello
• ci salutiamo = we greet each other

Here, ci is a reciprocal pronoun. It shows that the action goes both ways between the people involved.

It is built like a reflexive form, but here it is being used reciprocally.

That means:

• reflexive: the action comes back to yourself
  
  • mi lavo = I wash myself
• reciprocal: people do the action to one another
  
  • ci salutiamo = we greet each other

So in this sentence, ci does not really mean ourselves. It means each other.

Here quando means when, but in a general sense that can also feel like whenever.

So the sentence is not necessarily about one single moment. It can describe a habitual or typical situation:

• Quando ci salutiamo, il cane scodinzola.
• When we greet each other / Whenever we greet each other, the dog wags its tail.

Italian often uses the present tense like this for general truths or repeated actions.

Because Italian often uses the present tense to talk about:

• habits
• repeated actions
• general situations

So this sentence sounds like something that usually happens:

• quando ci salutiamo = when/whenever we greet each other
• il cane scodinzola = the dog wags its tail

This is very natural in Italian, just as English can say Whenever we greet each other, the dog wags its tail.

It can mean either, depending on context.

Most often, salutare means to greet / to say hello to. But in some contexts it can also mean to say goodbye to.

So:

• salutare qualcuno = to greet someone
• sometimes also = to say goodbye to someone

In this sentence, the intended meaning is probably greet each other, especially because of the dog happily wagging its tail.

Scodinzola comes from the verb scodinzolare, which means to wag its tail.

Here it is:

• scodinzolare = to wag one’s tail
• scodinzola = he/she/it wags its tail

Since the subject is il cane (the dog), scodinzola means the dog wags its tail.

Because the subject is singular:

• il cane = the dog

So the verb must also be singular:

• il cane scodinzola = the dog wags its tail

If the subject were plural, the verb would change:

• i cani scodinzolano = the dogs wag their tails

Italian usually needs an article before a noun in cases where English sometimes does not.

So il cane is the normal way to say the dog. It can refer to:

• a specific dog already known in the context
• sometimes a general, familiar animal in the situation

Saying just cane by itself would usually not work here.

Yes. Italian allows some flexibility.

For example, you could also say:

• Il cane scodinzola quando ci salutiamo.

This means the same thing. The version with Quando ci salutiamo first gives more emphasis to the time or situation. The version starting with Il cane puts the dog first.

Both are natural.

The comma is very common here because the sentence begins with a subordinate clause:

• Quando ci salutiamo, ...

That opening clause sets the scene, so a comma helps separate it from the main clause:

• Quando ci salutiamo, il cane scodinzola.

In informal writing, people are not always perfectly consistent with commas, but this punctuation is standard and helpful.

Not in this sentence.

Although ci can sometimes mean us in other structures, here it is part of salutarsi, so it has the reciprocal meaning each other.

So:

• ci salutiamo does not mean someone greets us
• it means we greet each other

The verb ending -iamo already tells you the subject is we.

Because Italian usually leaves out subject pronouns when the verb ending already makes the subject clear.

• salutiamo already means we greet
• scodinzola already means he/she/it wags

So Italian does not need to say noi here.

You could say noi ci salutiamo, but it would usually be for emphasis, not because it is grammatically necessary.