A colega com quem eu fiz a matrícula mora no mesmo bairro que eu.

Colega can refer to either a man or a woman. It is a noun with the same form for both genders, so the article shows the gender:

• o colega = a male colleague/classmate
• a colega = a female colleague/classmate

So in this sentence, a tells you the person is female.

Com quem means with whom.

It is a relative structure:

• com = with
• quem = whom / who

In Portuguese, when the relative pronoun refers to a person and comes after a preposition, quem is very common:

• a pessoa com quem falei = the person with whom I spoke
• a colega com quem fiz a matrícula = the classmate/colleague with whom I enrolled

Because the verb idea requires the preposition com.

You did the enrollment with that person, so Portuguese keeps the with:

• com quem eu fiz a matrícula

If you removed com, the relationship would change and the sentence would be ungrammatical or incomplete in this context.

In standard Portuguese, no. The normal structure is to place the preposition before the relative word:

• a colega com quem eu fiz a matrícula

This is one of the big differences from English. English often allows the preposition at the end: the classmate I enrolled with. Portuguese normally prefers the more fronted structure: com quem.

Yes, it could be left out.

Portuguese often drops subject pronouns when the verb already makes the subject clear. So this is also natural:

• A colega com quem fiz a matrícula mora no mesmo bairro que eu.

Including eu is not wrong at all. It can sound slightly clearer or a little more explicit, but it is not required.

In Brazilian Portuguese, fazer a matrícula is a common expression meaning to enroll or to complete registration/enrollment.

Literally, it looks like do the enrollment, but idiomatically it means carrying out that registration process.

A closely related alternative is:

• me matriculei = I enrolled

So this sentence could be rephrased in a similar way as:

• A colega com quem me matriculei...

though the original wording focuses more on doing the enrollment/registration process.

Portuguese often uses the definite article with nouns where English may be more flexible.

Here, a matrícula refers to a specific enrollment/registration event or process, not just the general concept of enrollment. So fazer a matrícula is a fixed, very natural expression.

You should think of it as one chunk:

• fazer a matrícula = to enroll / to register

No is a contraction of:

• em + o = no

And bairro is masculine:

• o bairro = the neighborhood

So:

• em o mesmo bairro becomes no mesmo bairro

Also, mesmo agrees with bairro, so it is masculine singular:

• o mesmo bairro
• compare with a mesma rua

Because there is an implied verb after eu.

The full idea is:

• mora no mesmo bairro que eu moro

Portuguese often omits the repeated verb because it is obvious. Since eu is the subject of the implied verb moro, you need the subject pronoun eu, not mim.

So:

• que eu = correct
• que mim = incorrect here

A useful comparison:

• Ela mora no mesmo bairro que eu.
• understood as: Ela mora no mesmo bairro que eu moro.

Yes, it would be grammatically correct.

But Portuguese often omits the repeated verb when it is obvious:

• mora no mesmo bairro que eu
• mora no mesmo bairro que eu moro

Both work, but the shorter version is usually more natural because it avoids repetition.

It describes a colega.

So the structure is:

• A colega = the classmate/colleague
• com quem eu fiz a matrícula = with whom I enrolled
• mora no mesmo bairro que eu = lives in the same neighborhood as I do

In other words, com quem eu fiz a matrícula is a relative clause that tells you which colleague we are talking about.

Not necessarily.

In Portuguese, colega is broader than English colleague. Depending on context, it can mean:

• classmate
• coworker
• peer
• colleague

Because the sentence mentions matrícula, many learners would understand colega here as something like classmate or fellow student, depending on the situation.