Learn Hardcore Dutch: Anna stelt de wekker in.

Because instellen is a separable verb. In main clauses, the particle splits off and goes to the end: Anna stelt … in. The base meaning is “to set, configure, program.”

Main clause: Anna stelt de wekker in.
Dictionary form: instellen (“to set/configure”)

Where does the particle go in other word orders (questions, subclauses, infinitives, perfect tense)?

Yes/no question (main clause): particle stays at the end
— Stelt Anna de wekker in?
Subordinate clause: the verb and particle fuse at the end
— … dat Anna de wekker instelt.
Te-infinitive: particle stands before te + infinitive
— Anna probeert de wekker in te stellen.
Perfect tense (past participle): prefix + stem + d/t
— Anna heeft de wekker ingesteld.

Can I also say Anna zet de wekker?

Yes. De wekker zetten is very idiomatic and common. Nuance:

De wekker zetten feels colloquial/everyday.
De wekker instellen can feel slightly more technical/precise (especially on devices). Both are fine in normal speech.

Why is it de wekker and not het wekker?

Wekker is a common-gender noun, so it takes de in singular: de wekker. Plural: de wekkers. Indefinite: een wekker.
Note: the diminutive is het wekkertje (all diminutives are het-words).

How do I mention the time it’s set to?

Use op with the time for setting:

Anna stelt de wekker in op 7 uur.
Anna zet de wekker op 7 uur.

Use om to say when it actually goes off:

De wekker gaat om 7 uur af.

How do I negate it?

Place niet before the particle at the end:

Anna stelt de wekker niet in.
With a time phrase: Anna stelt de wekker vandaag niet in.
“Never”: Anna stelt de wekker nooit in.

Is this verb reflexive? Do I need zich?

Not here. Iemand/iets instellen is transitive: you set something.
Be aware of a different expression: zich instellen op means “to adjust/brace oneself for.” That’s unrelated: We moeten ons instellen op vertraging.

How do I form the past and perfect?

Simple past: stelde
— Anna stelde de wekker in.
Perfect: auxiliary hebben
- ingesteld
  — Anna heeft de wekker ingesteld.

How do I turn it into a yes/no question?

Invert subject and finite verb; the particle stays at the end:

Stelt Anna de wekker in?

If I replace de wekker with a pronoun, do I use hem or het?

Since wekker is a de-word, the unstressed object pronoun is typically hem:

Anna stelt hem in.
In spoken Dutch, this is natural even for inanimate de-words. For a stressed/pointing form, you can use die: Anna stelt die in.

How do I say “the alarm goes off”?

Use the separable verb afgaan:

De wekker gaat om 7 uur af.
Perfect: De wekker is afgegaan.

Is there any difference between wekker and alarm?

Wekker = alarm clock (device) or the alarm on a device in everyday speech.
Alarm also exists and is common, especially for phones: een alarm zetten/instellen.
All are widely used; choose based on context and your preference.

Any pronunciation tips?

stelt: short e [ɛ], pronounce the final -t; cluster [stɛlt].
wekker: short e [ʊ]—actually [wɛkər], with a short first vowel and a schwa in the second syllable; double k keeps the vowel short.
in: like English “in,” but shorter/tenser [ɪn].
Regional r’s vary; both uvular and alveolar are fine.

How can I express the ongoing action (progressive)?

Dutch typically uses the simple present, but you can use the progressive with aan het to emphasize it’s in progress:

Neutral: Anna stelt de wekker in.
Progressive: Anna is de wekker aan het instellen.

What happens with modals or other auxiliaries?

With a modal, the particle stays with the infinitive at the end:
— Anna wil de wekker instellen.
With verbs that take te + infinitive:
— Anna probeert de wekker in te stellen.

How do I make an imperative?

Use the stem stel; put the object before the particle:

Stel de wekker in!
Polite/plural: Stelt u de wekker in, alstublieft.