En el campamento había otra familia con una tienda de campaña azul y una hoguera pequeña.

Because había is the form of haber used to mean there was / there were.

• había otra familia = there was another family
• estaba would mean was located / was for a specific thing already being talked about.
• era would describe what something was like or what it was.

So in this sentence, the speaker is introducing the existence of a family in the campsite, so había is the natural choice.

In standard Spanish, when haber means there is / there are / there was / there were, it stays in the singular.

So you say:

• había una familia = there was a family
• había dos familias = there were two families

Even with a plural noun, standard grammar keeps haber in this use singular.

Otra means another or other.

• otra familia = another family

It comes before the noun because it is a determiner/adjective commonly placed before the noun in Spanish in this kind of structure.

Compare:

• una familia = a family
• otra familia = another family

Tienda de campaña is the standard Spanish expression for tent.

Literally, it looks like:

• tienda = shop/store or tent, depending on context
• de campaña = of camping / for camp

But as a whole, tienda de campaña simply means tent. You should learn it as a fixed expression.

In Spain, tienda de campaña is the normal term.

Con means with.

Here it connects the family to the things they had with them:

• con una tienda de campaña azul y una hoguera pequeña
• with a blue tent and a small campfire

So it describes the family by mentioning what was associated with them.

In Spanish, most descriptive adjectives usually come after the noun.

So:

• una tienda de campaña azul = a blue tent

This is the normal order.
Putting azul before the noun would sound unusual here and would usually add a special stylistic effect rather than just simple description.

Both are possible, but they can feel slightly different.

• una hoguera pequeña = a small campfire
  This is the most neutral, straightforward description.
• una pequeña hoguera = a small little campfire
  This can sound a bit more subjective, expressive, or literary.

In this sentence, hoguera pequeña is just a plain factual description, so it fits well.

Because azul describes tienda de campaña, while pequeña describes hoguera.

The structure is:

• una tienda de campaña azul
• y
• una hoguera pequeña

So the y links the two noun phrases, not the two adjectives.

En el campamento means in the campsite / at the camp.

It sets the scene first: it tells you where everything is happening.

Spanish often places this kind of location phrase at the beginning of the sentence:

• En el campamento había...
• In the campsite there was...

This word order is very natural in Spanish.

Yes, absolutely.

Both are grammatical:

• En el campamento había otra familia...
• Había otra familia en el campamento...

The difference is mainly one of emphasis:

• En el campamento... puts the location first
• Había otra familia... puts the existence of the family first

The original sentence sounds very natural because it introduces the setting before mentioning what was there.

Spanish often uses the definite article where English may or may not use one.

So:

• en el campamento = in the campsite / at the campsite

This does not necessarily mean a special emphasis on the in English. It is just the normal Spanish way to refer to the place in this context.

Not exactly.

• fuego = fire
• hoguera = bonfire / campfire

In this sentence, hoguera is more specific because it refers to a fire set up outdoors, which fits the camping context.

So una hoguera pequeña is better than just un fuego pequeño here.

The imperfect is used here because the sentence describes a background scene or situation in the past.

It is not focusing on the moment when the family arrived. It is simply saying what was there.

So había works well for scene-setting:

• En el campamento había otra familia...
• There was another family at the campsite...

If you used a completed-action form, the sentence would feel more focused on an event happening, rather than on describing the setting.