Nie wiem, jak przebiega rekrutacja w tej firmie.

In this sentence, przebiega means something like goes, proceeds, or takes place step by step.

So jak przebiega rekrutacja is literally close to how the recruitment process goes or how recruitment proceeds.

The verb is przebiegać. In many contexts, it is used for the course of a process:

Jak przebiega spotkanie? = How is the meeting going?
Operacja przebiegła pomyślnie. = The operation went well.

So here it is not about physical running, even though the root is related to movement.

Jak means how here.

The clause jak przebiega rekrutacja w tej firmie means how recruitment works/goes in this company.

This is very natural in Polish after nie wiem:

Nie wiem, jak to działa. = I don’t know how it works.
Nie wiem, jak to zrobić. = I don’t know how to do it.

So jak introduces an indirect question, just like how in English.

In Polish, a comma is normally used before a subordinate clause, including an indirect question introduced by jak.

So:

Nie wiem, jak przebiega rekrutacja w tej firmie.

That comma is standard and expected. English does not always require a comma in the same place, so this is something learners often notice.

Tej firmie is in the locative case.

The preposition w often means in and requires the locative when it refers to location:

w firmie = in the company
w tej firmie = in this company

Here is the breakdown:

• ta firma = this company
• w tej firmie = in this company

So:

• ta changes to tej
• firma changes to firmie

Because Polish normally uses w with firma when you mean in a company / at a company.

So the natural expression is:

w firmie = in the company / at the company

Using na with firma would sound wrong in standard Polish.

This is just one of those preposition patterns that does not match English exactly. A useful pair to remember is:

pracuję w firmie = I work at a company
rekrutacja w tej firmie = recruitment in this company

Because rekrutacja is the subject of the clause jak przebiega rekrutacja.

In that clause, rekrutacja is the thing that proceeds / goes, so it stays in the nominative:

rekrutacja przebiega = recruitment proceeds

Even though the whole sentence starts with Nie wiem, the embedded clause still has its own grammar, and inside that clause rekrutacja is the subject.

Polish often uses the present tense for a general process or for something that is typically the case.

So jak przebiega rekrutacja w tej firmie means how recruitment works / how the recruitment process goes in this company in general.

It does not have to mean it is happening right this second. It can describe the usual procedure.

This is similar to English:

• I know how hiring works here.
• I don’t know how recruitment goes in this company.

Przebiega is the 3rd person singular present form of przebiegać.

That matches rekrutacja, which is a singular noun:

rekrutacja przebiega = recruitment proceeds

A quick mini-table:

• ja przebiegam
• ty przebiegasz
• on/ona/ono przebiega
• my przebiegamy
• wy przebiegacie
• oni/one przebiegają

In this sentence, the subject is rekrutacja, so Polish uses the same form as for ona: przebiega.

These are an aspect pair:

• przebiegać = imperfective
• przebiec = perfective

In this sentence, przebiegać is used because the speaker is asking about the course of the process in a general or ongoing sense.

Compare:

Nie wiem, jak przebiega rekrutacja w tej firmie.
= I don’t know how the recruitment process goes in this company.

Rekrutacja przebiegła sprawnie.
= The recruitment process went smoothly.

The second sentence uses the perfective past przebiegła, focusing on the process as a completed whole.

Yes, Polish word order is fairly flexible.

The given sentence is the most neutral and natural:

Nie wiem, jak przebiega rekrutacja w tej firmie.

But you could also say:

Nie wiem, jak w tej firmie przebiega rekrutacja.

That version puts a bit more attention on w tej firmie.

Both are correct, but the original version is probably the best one to learn first.

Yes. A very common alternative is:

Nie wiem, jak wygląda rekrutacja w tej firmie.

Literally, jak wygląda means what it looks like, but in Polish it often means what something is like / how something works in practice.

So:

• jak przebiega rekrutacja = how the recruitment process goes/proceeds
• jak wygląda rekrutacja = what the recruitment process is like

Both are natural. Przebiega sounds a bit more process-focused. Wygląda is slightly broader and very common in everyday speech.