أعمل مع الزملاء الذين يستعملون النظام الداخلي.

In Arabic, the subject pronoun is often built into the verb.

• أعمل = I work
• The أ at the beginning shows first person singular.

So أنا is not necessary unless you want emphasis or contrast.

• أعمل مع الزملاء... = I work with the colleagues...
• أنا أعمل مع الزملاء... = I work with the colleagues... with extra emphasis on I

مع means with.

So:

• أعمل مع الزملاء = I work with the colleagues / colleagues

After مع, the following noun is in the genitive case. In fully vowelled Arabic, you would see that in pronunciation, but in normal writing the short vowels are usually not written.

الزملاء is the plural of زميل (colleague).

This is a broken plural, not a regular sound masculine plural.

• singular: زميل
• plural: زملاء

Even though it is a broken plural in form, it refers to people, so Arabic often treats it grammatically as a plural of rational beings. That is why the relative pronoun and the verb after it are plural:

• الذين
• يستعملون

الذين means who or those who for a masculine plural (or mixed-gender plural in many contexts).

Here it refers back to الزملاء (the colleagues), so:

• الزملاء الذين... = the colleagues who...

This is the correct relative pronoun because the noun it refers to is:

• definite: it has ال
• plural
• human / rational

Normally, no.

In English, we can sometimes drop who/that:

• the colleagues who use the system
• the colleagues using the system

But in standard Arabic, after a definite noun, you normally need the relative pronoun:

• الزملاء الذين يستعملون...

If the noun were indefinite, Arabic would usually use a different structure instead of a relative pronoun.

Because it agrees with الذين, which refers to the colleagues.

• يستعملون = they use
• the ending -ون marks masculine plural in this kind of present-tense verb

So:

• الذين يستعملون = who use

The basic dictionary form is استعمل meaning to use.

Here is the breakdown:

• يستعمل = he uses
• يستعملون = they use

This verb is from Form X (استفعل pattern), though for a learner it is enough at this stage to recognize it as a common verb meaning use.

A very common synonym is يستخدمون from استخدم. So you may also see:

• الزملاء الذين يستخدمون النظام الداخلي

Both are natural.

Literally, it means something like:

• النظام = the system
• الداخلي = internal / inner

So together:

• النظام الداخلي = the internal system

Depending on context, it might also be understood as:

• the internal system
• the in-house system
• sometimes the internal regulations/bylaws, in other contexts

Here, since the meaning is already given, the important grammar point is that الداخلي is an adjective describing النظام.

Because Arabic adjectives usually match the noun they describe in definiteness.

So:

• نظام داخلي = an internal system
• النظام الداخلي = the internal system

Both the noun and the adjective are definite here, so both take ال.

This is very important in Arabic adjective phrases.

Yes. Arabic adjectives agree with the noun in:

• definiteness
• gender
• number
• case (in fully inflected Arabic)

Here:

• النظام is singular masculine definite
• الداخلي is also singular masculine definite

So they match.

Because الزملاء just means the colleagues or colleagues, depending on context.

• أعمل مع الزملاء = I work with the colleagues / with colleagues
• أعمل مع زملائي = I work with my colleagues

So if you want to explicitly say my colleagues, Arabic would usually use:

• زملائي

The sentence you were given does not explicitly say my.

It is a verbal sentence, because it begins with a verb:

• أعمل = I work

Then it continues with a prepositional phrase and a relative clause:

• مع الزملاء
• الذين يستعملون النظام الداخلي

So the structure is roughly:

• Verb
  • prepositional phrase
    • relative clause

In careful formal reading, it could be pronounced approximately as:

أعمَلُ معَ الزُّمَلاءِ الَّذينَ يَستَعمِلونَ النِّظامَ الدّاخِلِيَّ

A few notes:

• In normal everyday printed Arabic, these short vowels are usually not written.
• Learners often read the unvowelled version first and only later study the full endings.
• You do not need to produce full case endings perfectly in order to understand the sentence.

Yes, in standard grammar الذين is the plural relative pronoun mainly used for masculine plural.

For feminine plural, the formal form is:

• اللاتي or اللائي

However, in many real texts and in less formal usage, الذين may sometimes be used more broadly, especially for mixed groups or where masculine is the default.

In this sentence, الزملاء is a masculine (or mixed) plural group, so الذين is exactly right.