Szefowa ma włożyć umowę do niebieskiego segregatora, a kopie do szarego.

Yes. Szefowa is the feminine form of szef. It means a female boss / manager.

So:

• szef = a male boss, or sometimes a boss in a generic sense
• szefowa = a female boss

In this sentence, the person being talked about is clearly a woman.

Yes, ma is from mieć, which often means to have. But in the pattern mieć + infinitive, it can mean:

• is supposed to
• is to
• should
• sometimes has to

So Szefowa ma włożyć... means something like:

• The boss is supposed to put...
• The boss is to put...

It does not mean has put. Polish does not form the present perfect the way English does.

This is about aspect, which is very important in Polish.

• włożyć = perfective
  It focuses on a completed single action
• wkładać = imperfective
  It focuses on the process, repetition, or habit

Here the sentence is about putting the documents into the binders as a completed task, so włożyć is natural.

Compare:

• ma włożyć umowę = she is supposed to put the contract in
• ma wkładać umowy = she is supposed to be putting contracts in / put contracts in regularly

Because umowa is the direct object of the verb włożyć, so it takes the accusative case.

• nominative: umowa
• accusative: umowę

This is very common with feminine nouns ending in -a:

• książka → książkę
• teczka → teczkę
• umowa → umowę

Kopie is plural. It is the plural of kopia.

• singular: kopia = copy
• plural: kopie = copies

In this sentence it is also the direct object, so it is in the accusative plural. For this noun, the accusative plural looks the same as the nominative plural:

• nominative plural: kopie
• accusative plural: kopie

So a kopie do szarego means and the copies into the gray one.

After do, Polish normally uses the genitive case.

So:

• segregator → segregatora
• niebieski → niebieskiego

That gives:

• do niebieskiego segregatora = into/to the blue binder

With verbs like włożyć, Polish often uses do to express putting something into a container or place.

Because adjectives have to agree with the noun in gender, number, and case.

Here the noun is:

• segregator — masculine singular

And after do, it is in the genitive singular:

• segregatora

So the adjective must also be in masculine singular genitive:

• niebieski → niebieskiego
• szary → szarego

That is why we get:

• do niebieskiego segregatora
• do szarego segregatora → shortened in the sentence to do szarego

Because Polish can omit a noun when it is obvious from context.

So:

• do szarego really means do szarego segregatora

This works much like English the gray one, where one stands in for the noun. In Polish, the adjective itself can carry that meaning if the noun is understood.

Importantly, the adjective still keeps the form required by the missing noun:

• masculine singular genitive
• therefore szarego

In office Polish, segregator usually means a binder, often a ring binder or lever-arch file.

So this is not about segregation in the English sense. It is a very ordinary office-supplies word.

Here a links two contrasting or parallel pieces of information:

• the contract goes into the blue binder
• the copies go into the gray one

It is often translated as and, but it can also feel like:

• while
• whereas
• and as for

In this sentence, and is the most natural English translation.

Also, the comma before a is standard in Polish.

Not completely. Polish word order is more flexible than English because case endings show grammatical roles.

This sentence has a fairly neutral order:

• Szefowa ma włożyć umowę do niebieskiego segregatora, a kopie do szarego.

But other orders are possible if you want to emphasize something:

• Umowę szefowa ma włożyć do niebieskiego segregatora, a kopie do szarego.
• Do niebieskiego segregatora szefowa ma włożyć umowę...

Those versions shift emphasis, but the basic meaning stays the same.