Quand il fait froid, le chiot rentre vite dans sa niche et n’aboie plus.

In French, many weather expressions use faire:

• il fait froid = it is cold
• il fait chaud = it is hot
• il fait beau = the weather is nice

So il fait froid is the normal idiomatic way to talk about cold weather.
Il est froid usually means he/it is cold in the sense that a person or object is cold, not the weather.

Here quand can be understood as when or whenever, depending on context.

In this sentence, it describes a habitual situation, so in natural English it often feels like whenever:

• Quand il fait froid... = When/Whenever it is cold...

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

Both verbs are related, but they are not exactly the same:

• entrer = to enter, to go in
• rentrer = to go back in, to return inside, to go in

Rentre suggests the puppy goes back into its usual place, which fits well with sa niche.
So le chiot rentre dans sa niche gives the idea of the puppy going back into its doghouse.

Here une niche means a doghouse or kennel.

It can also mean a niche in other contexts, but with le chiot it clearly means the puppy’s little shelter.

Because niche is a feminine noun:

• une niche

French possessive adjectives agree with the thing possessed, not with the owner.

So:

• sa niche = his/her/its doghouse

Even though the puppy may be male, French uses sa because niche is feminine.

Vite is an adverb meaning quickly.

In French, short adverbs often come right after the conjugated verb:

• rentre vite = goes in quickly

That is the most natural position here.

Because the subject is still le chiot.

French, like English, can join two verbs with et when they have the same subject:

• le chiot rentre vite dans sa niche et n’aboie plus

This works like:

• The puppy goes quickly into its doghouse and no longer barks.

French does not need to repeat il or le chiot here.

Ne ... plus is a negative expression meaning:

• no longer
• not anymore

So:

• n’aboie plus = doesn’t bark anymore / no longer barks

Here it means that once the puppy goes into its doghouse, it stops barking.

Because aboie begins with a vowel sound.

In French, ne becomes n’ before a vowel or silent h:

• ne aboie → n’aboie

This is called elision.

No. In this sentence, plus is part of the negative expression ne ... plus, so it means:

• no longer
• not anymore

Compare:

• Je veux plus de pain. = I want more bread.
• Je ne veux plus de pain. = I don’t want any more bread / I no longer want bread.

So context is very important.

Aboie comes from the verb aboyer = to bark.

Here it is the third-person singular present tense:

• j’aboie
• tu aboies
• il/elle aboie

Since the subject is le chiot, the sentence uses aboie.

French often uses the present tense for habits, routines, and general truths.

So this sentence means something like a regular pattern:

• When it’s cold, the puppy quickly goes into its doghouse and stops barking.

This is completely normal in French.

It can be either, depending on context.

In this sentence, because of quand and the present tense, it most naturally describes a general or repeated situation:

• whenever it is cold, this is what the puppy does

So it sounds more like a habit than one single event.

In ne ... plus, the final s is usually not pronounced.

So plus here is usually pronounced roughly like plu.

That is different from some uses of plus meaning more, where the s may sometimes be heard.

Yes. In everyday spoken French, people often drop ne:

• Le chiot rentre vite dans sa niche et aboie plus.

That is very common in speech.
But in standard written French, ne ... plus is the correct full form.

Because dans means in/inside.

• dans sa niche = inside its doghouse

Since the puppy is going into the doghouse, dans is the natural preposition.
Using à would not give the same sense of being physically inside it.