Meine Kollegin synchronisiert den Ordner mit der Cloud, damit wir beide dieselbe Version haben.

Because Kollegin is a feminine noun, so the possessive has to match that gender in the nominative singular:

• mein Kollege = my male colleague
• meine Kollegin = my female colleague

Here Kollegin is also the subject of the sentence, so nominative is needed.

German main clauses usually follow the V2 rule: the finite verb goes in the second position.

So in:

• Meine Kollegin = first position
• synchronisiert = second position

The rest of the sentence follows after that. This is one of the most basic word-order rules in German main clauses.

Because Ordner is the direct object of synchronisiert, so it takes the accusative case.

• nominative: der Ordner
• accusative: den Ordner

You can think of it as: what is she synchronizing?
Answer: den Ordner.

Because the preposition mit always takes the dative case.

The noun Cloud is feminine:

• nominative: die Cloud
• dative: der Cloud

So:

• mit der Cloud = with the cloud

Yes, Cloud is commonly used in German, especially in tech contexts. It is normally treated as feminine: die Cloud.

German often assigns grammatical gender to borrowed words, and in this case standard usage is:

• die Cloud
• mit der Cloud

Learners just have to memorize the gender along with the noun.

Because damit introduces a subordinate clause, and in German subordinate clauses are separated from the main clause by a comma.

Main clause:

• Meine Kollegin synchronisiert den Ordner mit der Cloud

Subordinate clause:

• damit wir beide dieselbe Version haben

So the comma is required.

Here damit means so that and introduces a purpose clause.

So the structure is:

• She syncs the folder with the cloud
• so that we both have the same version

It explains the purpose of the action.

Because damit introduces a subordinate clause, and in German subordinate clauses usually send the finite verb to the end.

So instead of:

• wir beide haben dieselbe Version

you get:

• damit wir beide dieselbe Version haben

This is a very common pattern after subordinating conjunctions like weil, dass, obwohl, damit.

Wir beide is the natural and standard way to say both of us in German.

• wir beide = both of us

German normally places beide after the pronoun in this expression.
Beide wir sounds unnatural in standard German.

This is a very common learner question.

Strictly speaking:

• dieselbe = the very same, one identical thing
• die gleiche = the same kind/type, but not necessarily the identical item

So:

• dieselbe Version suggests one identical version shared by both people
• die gleiche Version can often be used in everyday speech too, but it is a little less precise

In real-life German, many speakers do not always keep this distinction strict, but in careful usage dieselbe is a good choice here.

Because dieselbe already includes the function of a definite article.

Compare:

• die Version = the version
• dieselbe Version = the same version

So dieselbe already carries the die- element inside it. That is why you do not say die dieselbe Version.

It is in the accusative case, because it is the direct object of haben in the subordinate clause.

The subject is:

• wir beide

What do we have?

• dieselbe Version

Since Version is feminine, nominative and accusative look the same here:

• nominative: dieselbe Version
• accusative: dieselbe Version

So the form does not change visibly, but the function is accusative.

German present tense often covers both simple present and present progressive meanings.

So synchronisiert can mean:

• synchronizes
• is synchronizing

Which English translation fits best depends on context. German usually does not need a separate form like English is synchronizing.

Not naturally in this sentence, because um...zu is usually used when the subject of both clauses is the same.

For example:

• Ich lerne Deutsch, um in Berlin zu arbeiten.
  • I study German in order to work in Berlin.

But here the subjects are different:

• main clause subject: meine Kollegin
• subordinate clause subject: wir beide

So damit is the right choice:

• ..., damit wir beide dieselbe Version haben.

It breaks down like this:

Main clause:

• Meine Kollegin = subject
• synchronisiert = finite verb
• den Ordner = direct object
• mit der Cloud = prepositional phrase

Subordinate clause of purpose:

• damit = so that
• wir beide = subject
• dieselbe Version = object
• haben = verb at the end

So the full structure is:

[Main clause], [subordinate clause]

which is very typical German sentence building.