الجبل قرب البحيرة وخارج المخيم.

Because Arabic often leaves out the verb to be in the present tense.

So:

• الجبل قرب البحيرة = The mountain is near the lake
• الجبل خارج المخيم = The mountain is outside the camp

This is called a nominal sentence. In the present tense, Arabic normally does not use a separate word for is/am/are.

If you wanted a past-tense meaning, then Arabic would use a verb, for example:

• كان الجبل قرب البحيرة = The mountain was near the lake

The sentence is:

• الجبل = the subject
• قرب البحيرة وخارج المخيم = the predicate / what is being said about the mountain

More specifically:

• الجبل = the mountain
• قرب البحيرة = near the lake
• وخارج المخيم = and outside the camp

So the whole sentence means that the mountain has two location descriptions:

1. it is near the lake
2. it is outside the camp

Word by word:

• الجبل = the mountain
• قرب = near / nearby to
• البحيرة = the lake
• و = and
• خارج = outside
• المخيم = the camp

So literally, it is something like:

• the mountain near the lake and outside the camp

Natural English: The mountain is near the lake and outside the camp.

They are definite because the sentence is referring to a specific lake and a specific camp:

• البحيرة = the lake
• المخيم = the camp

If you removed الـ, the meaning would become more indefinite:

• قرب بحيرة = near a lake
• خارج مخيم = outside a camp

So the definite article الـ works much like the in English.

They are often taught like prepositions in beginner materials because they function like English near and outside, but grammatically they are often analyzed as nouns of place / adverbial expressions in Arabic.

That is why they are commonly followed by a noun in the genitive:

• قرب البحيرة
• خارج المخيم

For a learner, the easiest practical approach is:

• learn قرب + noun = near ...
• learn خارج + noun = outside ...

So even if the deeper grammar is a little different from simple prepositions, you can safely use them this way.

Because Arabic puts these location expressions before the thing they relate to, just as English does:

• near the lake
• outside the camp

In Arabic:

• قرب البحيرة
• خارج المخيم

So the pattern is:

• قرب + place
• خارج + place

This is the normal order.

Because و simply joins the two predicate phrases:

• قرب البحيرة
• خارج المخيم

So the sentence structure is:

• الجبل
  • near the lake
    • and
      • outside the camp

Arabic does not need to repeat الجبل. English also usually does not repeat the subject here:

• The mountain is near the lake and outside the camp.

Not:

• The mountain is near the lake and the mountain is outside the camp.

In fully vowelled MSA, it would commonly be:

• الجبلُ قربَ البحيرةِ وخارجَ المخيمِ

A basic explanation:

• الجبلُ has ـُ because it is the subject
• قربَ and خارجَ are often treated here as adverbial expressions, so they take ـَ
• البحيرةِ and المخيمِ take ـِ because they come after these expressions in a genitive relationship

In normal everyday writing, these short vowel endings are usually omitted, so you will often just see:

• الجبل قرب البحيرة وخارج المخيم

Yes. In many contexts, قرب can be translated as:

• near
• close to
• in the vicinity of

So:

• الجبل قرب البحيرة
  can be understood as
• The mountain is near the lake
• The mountain is close to the lake

Near is usually the simplest and most natural translation for learners.

Yes, but the given order is very natural.

The sentence begins with الجبل because that is the topic: the mountain.

You may also see Arabic start with a location phrase for emphasis in some contexts, but for a straightforward learner sentence, this order is best:

• الجبل قرب البحيرة وخارج المخيم

It clearly means:

• first, identify the thing: the mountain
• then describe where it is

So this is a good standard model to follow.