Ana semnează formularul, iar eu fac o copie pentru Andrei.

Because Romanian usually puts the definite article at the end of the noun instead of before it.

• formular = form / a form
• formularul = the form

So Ana semnează formularul means Ana signs the form.

This is a very common feature of Romanian:

• băiat = boy
• băiatul = the boy
• carte = book
• cartea = the book

Here, iar links the two parts of the sentence and shows a mild contrast or parallel between them.

In this sentence, it is close to:

• and
• while
• whereas

So:

• Ana semnează formularul, iar eu fac o copie... can be understood as:
• Ana signs the form, and I make a copy...
• Ana signs the form, while I make a copy...

Compared with other connectors:

• și = simple and
• dar = but
• iar often sounds a bit more contrastive or balanced than și

That is correct: Romanian often leaves out subject pronouns because the verb ending already shows the person.

So fac already means I do / I make.

However, eu is added here for emphasis or contrast:

• Ana does one action,
• eu do another.

So iar eu sounds natural because it highlights the contrast:

• Ana signs the form, and I make a copy...

Without eu, the sentence would still be grammatical:

• Ana semnează formularul, iar fac o copie pentru Andrei.

But with eu, the contrast is clearer and more natural in this context.

They are both in the present tense.

• semnează = he/she signs
• fac = I do / I make

More specifically:

• Ana semnează = Ana signs
• eu fac = I make / I do

These are present indicative forms.

Because o here means a / one and acts as the indefinite article for a feminine singular noun.

• copie = copy
• o copie = a copy

So:

• fac o copie = I make a copy

This is similar to:

• o carte = a book
• o masă = a table

Be careful: o can also mean it in other contexts, but here it is simply the article a.

Yes. Romanian can also use a copia = to copy.

But a face o copie is a very common and natural expression, especially when talking about making a physical or digital copy of a document.

So these are both possible, depending on context:

• fac o copie = I make a copy
• copiez formularul = I copy the form

In your sentence, fac o copie emphasizes producing a copy, which matches English make a copy very well.

Pentru means for.

So:

• pentru Andrei = for Andrei

It shows who the copy is intended for.

This is the normal way to express this idea:

• un cadou pentru Maria = a gift for Maria
• o scrisoare pentru profesor = a letter for the teacher

So fac o copie pentru Andrei means the copy is made on Andrei’s behalf or intended for him.

Yes, Romanian has more flexible word order than English, although the version you have is very natural and neutral.

The basic order here is:

• Ana (subject)
• semnează (verb)
• formularul (object)

and then:

• eu (subject)
• fac (verb)
• o copie (object)
• pentru Andrei (prepositional phrase)

You could move things around for emphasis, but the original sentence is the most straightforward:

• Ana semnează formularul, iar eu fac o copie pentru Andrei.

Romanian often changes word order to emphasize a particular element, but learners should usually start with this more neutral pattern.

Yes. It comes from the verb a semna, which means to sign.

So:

• a semna = to sign
• semnez = I sign
• semnezi = you sign
• semnează = he/she signs

You may also see:

• semnătură = signature

So these words belong to the same general idea.

Because Ana and Andrei are proper names, and Romanian normally does not use an article with personal names in neutral standard usage.

So:

• Ana = Ana
• Andrei = Andrei

Romanian does sometimes use articles or special forms with names in certain regional or informal speech, but in standard sentences like this, the plain name is normal.

You could replace iar with și:

• Ana semnează formularul și eu fac o copie pentru Andrei.

That means:

• Ana signs the form and I make a copy for Andrei.

However, iar is a little better here because it neatly sets up two parallel actions by two different people:

• Ana does one thing,
• I do another.

So the original version sounds slightly more elegant and natural in this context.