Learn Hardcore German: Wir dürfen jederzeit Fragen stellen.

Because dürfen is a modal verb. In a main clause with a modal, the finite modal goes in the second position and the main verb appears at the end in the infinitive:

Subject + modal (2nd) + … + infinitive at the end. Here: Wir (subject) + dürfen (modal) + … + stellen (infinitive at the end).

What nuance does dürfen have compared with können?

dürfen = to be allowed to, permission (like English “may”).
können = to be able to, ability/possibility (like English “can”). For permission, German prefers dürfen. Colloquially you’ll hear können used for permission, but in careful/standard speech use dürfen, especially in questions:
Darf ich eine Frage stellen? = May I ask a question? (preferred)
Kann ich eine Frage stellen? = Can I ask a question? (colloquial, less precise)

Why say Fragen stellen instead of just fragen?

German often uses the collocation eine Frage stellen (“to ask a question”). With a plural, it becomes Fragen stellen (“to ask questions”).

fragen is the verb “to ask (someone)”, e.g., Ich frage ihn.
To say “ask a question,” use eine Frage stellen, not “eine Frage fragen.”
Your sentence emphasizes the act of posing questions (possibly multiple).

Do I need an article before Fragen here?

No. German uses no article for an indefinite plural of countable nouns. Fragen alone means “questions” in general.
Add an article or determiner if you want to specify:

die Fragen = the questions
einige Fragen = some questions
keine Fragen = no questions

What case is Fragen in, and why?

Accusative plural. The verb stellen takes a direct object (accusative), and Fragen is that object. In the plural, feminine nouns like die Frage take the ending -n in both nominative and accusative: die Fragen.

Why is Fragen capitalized?

All nouns are capitalized in German. Fragen is the plural of the feminine noun die Frage (“question”).

Where can jederzeit go in the sentence?

jederzeit is an adverb. Neutral options include:

Wir dürfen jederzeit Fragen stellen. (very natural)
Jederzeit dürfen wir Fragen stellen. (fronted for emphasis on “at any time”)
Wir dürfen Fragen jederzeit stellen. (also possible; slightly different rhythm) Fronting or moving it changes emphasis, not the core meaning.

How does jederzeit differ from immer?

jederzeit = at any time (availability at all times; you can choose the time freely)
immer = always/constantly (without interruption or on every occasion)
Often interchangeable contextually, but jederzeit stresses freedom of timing; immer stresses continuity/habit.

How would I make this a yes/no question?

Invert the subject and the finite verb:

Dürfen wir jederzeit Fragen stellen?

How do I negate this, and what’s the difference between options?

Wir dürfen nicht jederzeit Fragen stellen. = We’re not allowed to ask questions at all times (only at certain times).
Wir dürfen keine Fragen stellen. = We’re not allowed to ask any questions (not at all).
Avoid Wir dürfen jederzeit keine Fragen stellen unless you specifically mean “At any time, we’re to ask no questions,” which is unusual and confusing.

How do I say it in the past or as a polite conditional?

Simple past (permission in the past): Wir durften jederzeit Fragen stellen.
Polite conditional (Konjunktiv II): Dürften wir jederzeit Fragen stellen? (very polite request)

What happens in a subordinate clause?

Both verbs move to the end, with the modal last:

…, dass wir jederzeit Fragen stellen dürfen.
Word order: … subordinate conjunction + subject + … + main verb (infinitive) + modal (infinitive/finite as required) at the end.

How do I form the perfect with a modal here?

Use the double-infinitive construction:

Wir haben jederzeit Fragen stellen dürfen.
The auxiliary is haben, and both stellen and dürfen appear at the end. (Perfect of modals without a dependent infinitive is rare in modern usage.)

Is jederzeit one word? Can I write jeder Zeit?

It’s one word: jederzeit.
You can say zu jeder Zeit (“at every/any time”) as a two-word phrase with a preposition, but plain jeder Zeit without zu is incorrect.

Could I generalize the statement with man instead of wir?

Yes: Man darf jederzeit Fragen stellen.
This means “One may/People may ask questions at any time,” making it a general rule rather than about “we.”

How would I express this as an instruction/encouragement?

Informal plural: Stellt jederzeit Fragen!
Formal: Stellen Sie jederzeit Fragen!
If you want to keep the permission tone: Ihr dürft jederzeit Fragen stellen. / Sie dürfen jederzeit Fragen stellen.

Any common pitfalls to avoid with these words?

Don’t say eine Frage fragen; say eine Frage stellen.
Use dürfen (permission) rather than können in careful speech when asking for or granting permission.
Keep jederzeit as one word.
Remember verb position with modals: finite modal in 2nd position, main verb at the end.