Learn Hardcore Finnish: Pidä henkilökortti mukana, kun menet virastoon. - Keep your ID card with you when you go to the office.

Pidä is the 2nd person singular imperative of the verb pitää (to keep/hold). It’s the form you use when telling one person what to do: (Sinä) pidä… = Keep… / Make sure you have…
The dictionary form is pitää, but imperatives often have their own stem (here pid-).

Is this imperative polite, or does it sound like an order?

In Finnish, the plain imperative (Pidä…) can be neutral: it can sound like an instruction, a reminder, or a mild command depending on context and tone.
If you want a more explicitly polite/customer-service style, Finnish often uses:

Pitäkää henkilökortti mukana… (imperative for te, used politely to strangers)
or softer phrasing like Kannattaa pitää henkilökortti mukana… (It’s a good idea to…)

Why is henkilökortti in this form (not changed), and what case is it?

henkilökortti is the object of pidä. Here it appears in the basic nominative-looking form, but functionally it’s the imperative object in a non-total (partitive-like) command meaning “keep (it) with you” rather than “take/complete it.”
In many “keep/have” instructions, Finnish commonly uses this kind of object form with an imperative.

Could it be Pidä henkilökorttia mukana instead?

Yes, Pidä henkilökorttia mukana is also possible, and it leans more clearly toward partitive: “keep some ID with you / keep carrying your ID (as an ongoing habit).”
Pidä henkilökortti mukana sounds very natural when you mean a specific item: “keep your (the) ID card with you.”

What exactly does mukana mean here?

mukana means with you / along / in your possession. It’s an adverb used to express “having something with you”:

Pidä X mukana = “Keep X with you / Bring X along” It doesn’t need a separate word for “with” the way English does.

Why is there a comma before kun?

Because kun menet virastoon is a subordinate clause (“when you go to the office”), and Finnish normally separates a main clause and a subordinate clause with a comma:

Pidä henkilökortti mukana, kun menet virastoon.

Does kun mean when or because here?

kun can mean when or because, depending on context.
Here, with a going-to-somewhere action (menet virastoon), it’s clearly temporal: when.
If the clause expressed a reason, it could be because (e.g., “Do X, since Y is true”), but that’s not the natural reading here.

What form is menet?

menet is the 2nd person singular present tense of mennä (to go):

(sinä) menet = you go / you are going
Finnish present tense often covers what English expresses with either present simple or present continuous, and context decides.

Why is it virastoon and not virastossa or virastolle?

Because virastoon is the illative case, expressing movement into a place:

virasto = office (government/administrative office)
virastoon = into the office (destination)

Compare:

virastossa (inessive) = in the office (location)
virastolle (allative) = to the office in the sense of “to the office area/office as a point,” but for buildings/rooms Finnish very often prefers -Vn/-seen (virastoon) for going inside.

Is virasto just any “office,” like a workplace?

Usually virasto refers to an official/public administration office (a bureau, agency office, municipal office), not a random private company office.
A regular workplace office is often toimisto. So virastoon strongly suggests something like a government service office.

Could I change the word order—does it matter?

You can change it, but the neutral, natural instruction is exactly what you see:

Pidä henkilökortti mukana, kun menet virastoon.

Other orders are possible for emphasis:

Kun menet virastoon, pidä henkilökortti mukana. (puts emphasis on the “when you go…” condition) Finnish word order is flexible, but it’s used to manage focus and emphasis, not random variation.

How would this differ from using ota (“take”) instead of pidä?

They’re close but not identical:

Ota henkilökortti mukaan, kun menet virastoon. = Take your ID with you when you go… (focus on remembering to take it at departure)
Pidä henkilökortti mukana… = Keep/have it with you (focus on carrying it with you as you go)

Both are natural; ota mukaan is especially common as a reminder right before leaving.

What are the key pronunciation things to watch in this sentence?

A few common learner points:

Pidä: the ä is like the vowel in English cat (but cleaner), and it’s long-ish if written long (here it’s single ä, normal length).
henkilökortti: stress is on the first syllable: HEN-ki-lö-KORT-ti.
virastoon: note the long oo sound (written oo) and the -n at the end: vi-ras-toon.