حقيبة الإسعافات الأولية جاهزة في المخيم.

In the present tense, Arabic usually does not use a separate word for is / are in simple statements like this.

So:

• حقيبة الإسعافات الأولية جاهزة
  literally: The first-aid bag ready naturally: The first aid kit is ready

This is called a nominal sentence. It has:

• a topic / subject: حقيبة الإسعافات الأولية
• a predicate: جاهزة
• an extra prepositional phrase: في المخيم

If you wanted was, then Arabic would use كان:

• كانت حقيبة الإسعافات الأولية جاهزة في المخيم = The first aid kit was ready at the camp

A simple way to break it down is:

• حقيبة الإسعافات الأولية = the first aid kit
• جاهزة = ready
• في المخيم = in / at the camp

So the overall pattern is:

• [noun phrase] + [predicate adjective] + [prepositional phrase]

More traditionally:

• حقيبة الإسعافات الأولية = المبتدأ (the topic/subject)
• جاهزة = الخبر (the predicate)
• في المخيم = a phrase giving location

Because this is an iḍāfa construction, often called a genitive construction or X of Y structure.

• حقيبة = bag
• الإسعافات الأولية = the first aid

Together:

• حقيبة الإسعافات الأولية
  literally: bag of the first aid naturally: the first aid kit

In an iḍāfa:

• the first noun usually does not take الـ
• the whole phrase can still be definite if the second part is definite

So حقيبة has no الـ, but the whole phrase is still definite because الإسعافات الأولية is definite.

Yes. Very often Arabic expresses noun combinations with an of structure.

So:

• حقيبة الإسعافات الأولية
  literally = bag of the first aid / bag of first aid supplies idiomatically = first aid kit

This is very common in Arabic. English often prefers a compact noun phrase like first aid kit, but Arabic often uses iḍāfa instead.

Other similar patterns:

• باب البيت = the door of the house = the house door
• مدير المدرسة = the director of the school = the school principal

Because it describes حقيبة, and حقيبة is a feminine singular noun.

You can often recognize feminine nouns by ـة (tāʾ marbūṭa) at the end:

• حقيبة = bag, feminine

So the adjective must agree with it:

• جاهز = ready, masculine singular
• جاهزة = ready, feminine singular

That is why the sentence says:

• حقيبة ... جاهزة

not

• حقيبة ... جاهز

This is a very common Arabic pattern.

الإسعافات is a non-human plural noun. In Modern Standard Arabic, non-human plurals are very often treated grammatically like feminine singular when they take adjectives.

So:

• الإسعافات = plural
• but its adjective is الأولية = feminine singular

That is why you get:

• الإسعافات الأولية

This may feel strange to English speakers, but it is normal Arabic grammar.

Compare:

• الكتب الجديدة = the new books
• السيارات السريعة = the fast cars

Even though the nouns are plural, the adjective often appears in the feminine singular form when the plural is non-human.

Because الأولية is an adjective describing الإسعافات, and adjectives normally match the noun they describe in definiteness as well as gender and number.

So:

• الإسعافات is definite because it has الـ
• therefore the adjective is also definite:
  • الأولية

So the phrase is:

• الإسعافات الأولية

not

• الإسعافات أولية

في most basically means in, but in many contexts it can also be translated naturally as at.

So:

• في المخيم can mean:
  • in the camp
  • at the camp

Which English translation sounds better depends on context.

For location statements like this, English often prefers at the camp, while Arabic simply uses في very naturally.

If fully vocalized, the sentence would be:

• حقيبةُ الإسعافاتِ الأوَّليةِ جاهزةٌ في المخيمِ

Here is why:

• حقيبةُ → ḍamma because it is the subject/topic of the nominal sentence
• الإسعافاتِ → kasra because it is the second part of the iḍāfa
• الأوَّليةِ → kasra because it follows الإسعافات and agrees with it
• جاهزةٌ → usually ḍamma because it is the predicate
• المخيمِ → kasra because it comes after the preposition في

In normal everyday writing, these short vowel endings are usually omitted.

A careful pronunciation would be something like:

• ḥaqībatu l-isʿāfāti l-awwaliyati jāhizatun fī l-mukhayyami

A more learner-friendly breakdown:

• حقيبة = ḥa-qī-ba
• الإسعافات = al-is-ʿā-fāt
• الأولية = al-aw-wa-liy-ya
• جاهزة = jā-hi-za
• في المخيم = fī al-mu-khay-yam

A few pronunciation notes:

• ح is a deeper h sound than English h
• ع in إسعافات is a consonant English does not really have
• خ in المخيم is like the ch in German Bach or Scottish loch
• يّ in المخيّم is doubled, so you hold it slightly longer

Yes, Arabic word order is somewhat flexible, though the sentence you have is very natural.

Standard order here:

• حقيبة الإسعافات الأولية جاهزة في المخيم

You could also move the location for emphasis:

• في المخيم حقيبة الإسعافات الأولية جاهزة

That might feel like:

• At the camp, the first aid kit is ready

But for most learners, the original version is the best neutral pattern to use.

You would usually make the noun phrase indefinite. One possible form is:

• حقيبةُ إسعافاتٍ أوليةٍ جاهزةٌ في المخيم

Here the phrase is no longer definite:

• حقيبة = a bag
• إسعافاتٍ أوليةٍ = first-aid supplies / first aid, indefinite

So the meaning becomes more like:

• A first aid kit is ready in the camp

The original sentence, with الإسعافات الأولية, is definite and naturally understood as the first aid kit.