Moja šefica i moja koleginica često razgovaraju na poslu.

Because moja has to agree with the noun it describes.

Both šefica and koleginica are feminine singular nouns in the nominative case, so the possessive adjective also takes the feminine singular nominative form: moja.

Compare:

• moj šef = my boss, masculine
• moja šefica = my boss, feminine

So Serbian possessives change form depending on gender, number, and case.

Repeating moja makes the sentence clearer.

Moja šefica i moja koleginica most naturally means two different women:

• my boss
• my colleague

If you said moja šefica i koleginica, it could sound more ambiguous, and some listeners might understand it as one woman who is both your boss and your colleague.

So the repetition is a very natural way to show that these are two separate people.

Yes.

• šefica = female boss
• koleginica = female colleague

The corresponding masculine forms are:

• šef = male boss
• kolega = male colleague

So the sentence specifically tells us that both people are women.

Each noun refers to one person, so each one stays singular:

• moja šefica = one woman
• moja koleginica = one woman

Together, they form a compound subject, and that is why the verb becomes plural:

• razgovaraju = they talk / they are talking

So the nouns are singular individually, but the whole subject is plural.

Because the subject is plural: my boss and my colleague.

Razgovaraju is the 3rd person plural present tense of razgovarati.

A quick comparison:

• ona razgovara = she talks
• one razgovaraju = they talk

Since there are two women in the subject, Serbian uses the plural verb form.

The basic form is razgovarati, meaning to talk / to converse.

In Serbian, the present tense often covers both meanings that English separates into:

• they talk
• they are talking

Context tells you which meaning is intended.

Here, because of često = often, the meaning is clearly habitual:

• They often talk at work

So in this sentence, it is not really are talking right now, but rather they often talk.

Često is an adverb meaning often.

It tells you how frequently the action happens.

So:

• razgovaraju = they talk
• često razgovaraju = they often talk

Its position before the verb is very natural and neutral in Serbian.

Yes, Serbian word order is fairly flexible.

The version you have is neutral and natural:

• Moja šefica i moja koleginica često razgovaraju na poslu.

But other orders are possible for emphasis, for example:

• Na poslu moja šefica i moja koleginica često razgovaraju.
• Moja šefica i moja koleginica razgovaraju često na poslu.

That said, the original word order sounds the most standard and natural for a learner to use.

Na poslu is the normal Serbian expression for at work.

Literally, it looks like on work / on the job, but idiomatically it means at work.

This is just the expression Serbian uses, so it is best learned as a set phrase:

• na poslu = at work

English learners often want to say something closer to in work, but Serbian normally uses na poslu here.

Because after na when it means location, Serbian uses the locative case.

The dictionary form is:

• posao = job, work

But in the locative singular, it becomes:

• poslu

So:

• na poslu = at work

This noun also changes its stem a bit in other cases:

• posao
• posla
• poslu
• poslom

So poslu is just the correct case form after na in this expression.

Because Serbian does not have articles like English.

So Serbian does not normally say separate words for:

• a boss
• the boss

Instead, meaning comes from context, and sometimes from words like:

• moj / moja = my
• ovaj / ova = this
• taj / ta = that

In your sentence, moja already makes the meaning specific, so no article is needed.

No.

In English, we often say talk with each other, but in Serbian that is not necessary here. The subject itself already shows the two people involved:

• Moja šefica i moja koleginica razgovaraju...

That naturally implies they are talking to each other.

If you wanted to make it explicit, you could say something like:

• Moja šefica i moja koleginica često razgovaraju jedna s drugom na poslu.

But that is more explicit than necessary in this sentence.

A few useful ones from this sentence:

• š sounds like sh in ship
• č sounds like ch in church
• j sounds like y in yes

So roughly:

• šefica ≈ shefitsa
• često ≈ chesto
• moja ≈ moya

These are only rough English approximations, but they are a good start.