Learn Hardcore German: In der Filiale bekomme ich das Formular ausgedruckt und kriege es gleich mit. - At the branch I get the form printed for me and get to take it with me immediately.

Both mean to get/receive.
bekommen is neutral/standard and works in all contexts.
kriegen is colloquial/informal; very common in speech but best avoided in formal writing. A formal alternative is erhalten.
Your sentence mixes them just for stylistic variety: you could use bekommen twice as well.

What does the structure das Formular ausgedruckt bekommen mean?

This is the so‑called recipient passive (bekommen-Passiv/Rezipientenpassiv). It highlights that you receive the result of someone else’s action.

Active: Jemand druckt mir das Formular aus.
Regular passive: Das Formular wird (für mich) ausgedruckt.
Recipient passive: Ich bekomme das Formular ausgedruckt. (I get it printed for me.)

Why is ausgedruckt at the end in bekomme ich das Formular ausgedruckt?

German places non-finite verb parts (participles/infinitives) at the end of the clause. Here, bekomme is the finite verb in position 2, and ausgedruckt (participle of ausdrucken) goes to the sentence-final position.

Main clause: Ich bekomme das Formular ausgedruckt.
Subordinate clause: ..., dass ich das Formular ausgedruckt bekomme.

Could I use gedruckt instead of ausgedruckt?

ausdrucken = print out (typically from a computer/printer).
drucken = print (more general; also mass printing). In everyday office contexts with forms, ausdrucken is the most idiomatic: das Formular ausdrucken/ausgedruckt. gedruckt wouldn’t be wrong, but it sounds less specific.

What exactly does kriege es gleich mit mean, and what does mit do?

mit- is a separable prefix meaning “with/along.”
(etw.) mitbekommen/mitkriegen means “to be given something to take along/with you.” So Ich kriege es gleich mit = “I get it right away to take with me.”
Contrast: mitnehmen = “to take something with you (actively, by yourself).” Here, the staff gives it to you—hence mitbekommen/mitkriegen, not mitnehmen.

Can I use bekommen both times for consistency?

Yes. For example:

In der Filiale bekomme ich das Formular ausgedruckt und bekomme es gleich mit. That’s perfectly fine (just a bit repetitive). Many speakers prefer the variation with kriegen in speech.

How is gleich different from sofort here?

Both can mean “immediately/right away.”

sofort is unequivocally “without delay.”
gleich often means “right away,” but can also soften to “in a moment/very soon” depending on context. In your sentence, it means “right away.” Note gleich can also mean “same/equal” in other contexts (e.g., das gleiche).

Why is it in der Filiale (dative) and not accusative?

in is a two-way preposition:

Dative for location (Wo?): in der Filiale = at/in the branch.
Accusative for motion (Wohin?): in die Filiale = into the branch.

Could I say bei der Filiale instead of in der Filiale?

Usually no. bei is “at/near (someone/some place)” and is common with institutions or people: bei der Bank, bei der Post. When you mean inside the branch premises, in der Filiale is the natural choice.

Why is the subject after the verb in In der Filiale bekomme ich ...?

German main clauses are verb‑second (V2). If you put an adverbial like In der Filiale first, the finite verb must still be second, so the subject ich comes after the verb:

In der Filiale (slot 1) bekomme (slot 2) ich ...

Do I need a comma before und kriege?

No. Because the subject isn’t repeated (it’s still ich), you normally do not set a comma:

In der Filiale bekomme ich das Formular ausgedruckt und kriege es gleich mit. If you explicitly repeat the subject, a comma is possible:
In der Filiale bekomme ich das Formular ausgedruckt, und ich kriege es gleich mit.

Can I drop the es in kriege es gleich mit?

No. German generally requires object pronouns; you can’t omit es here. Either repeat the noun (kriege das Formular gleich mit) or use the pronoun (kriege es gleich mit).

What gender is Formular, and is es the correct pronoun?

Formular is neuter: das Formular. The correct accusative/neuter pronoun is es, hence kriege es.

Is kriegen acceptable in formal German?

In formal writing or careful speech, prefer bekommen or erhalten. kriegen is widely used in everyday conversation, but it’s colloquial in tone.

Where does gleich go in the clause, and can it go after mit?

Place gleich before the separable prefix:

Correct: Ich kriege es gleich mit.
Wrong: Ich kriege es mit gleich. The prefix mit must be the final element of the separable verb in main clauses.

How do I say this in the past (Perfekt)?

In der Filiale habe ich das Formular ausgedruckt bekommen und habe es gleich mitbekommen. Colloquial alternative with kriegen:
… habe ich das Formular ausgedruckt bekommen und habe es gleich mitgekriegt.

Is there a difference between mitkriegen and mitbekommen?

They’re near‑synonyms. Both can mean “to notice” or “to receive (to take with you).”

mitbekommen is a bit more neutral.
mitkriegen is more colloquial. In your sentence, either is fine: … und bekomme/kriege es gleich mit.

Are there alternative phrasings without bekommen/kriegen?

Yes:

In der Filiale druckt man mir das Formular aus, und ich nehme es gleich mit. (more active “I take it with me”)
In der Filiale wird mir das Formular ausgedruckt, und es wird mir gleich ausgehändigt/mitgegeben. (passive/formal)