Learn Hardcore Dutch: Gelukkig repareerde een technicus het alarm nog dezelfde avond. - Fortunately, a technician repaired the alarm the same evening.

In Dutch main clauses the finite (conjugated) verb must occupy the second position (the “V2-rule”). You can choose any single element to place in the first slot—here the adverb Gelukkig—and then the verb repareerde follows in slot two. The subject een technicus comes third. If you had started with the subject, it would look like this:
• Een technicus repareerde gelukkig het alarm nog dezelfde avond.

What is the function of nog in nog dezelfde avond?

Here nog is a time-adverbial meaning “still” or “even,” pointing out that the repair took place on that same evening (i.e. sooner than you might have expected). It ties together with dezelfde avond (“that same evening”) and emphasizes the promptness of the action.

Why is it dezelfde avond instead of hetzelfde avond? Could I also say nog diezelfde avond?

dezelfde must agree with the grammatical gender of the noun it modifies. Since avond is a de-woord (common gender), you use dezelfde. If it had been a het-woord, you would say hetzelfde (e.g. hetzelfde huis).
You can also use nog diezelfde avond, where diezelfde (“that very same”) adds a demonstrative, slightly more emphatic nuance than the neutral dezelfde.

Why do we need the indefinite article een before technicus, whereas English sometimes omits it?

Dutch almost always requires an article (definite de/het or indefinite een) with singular countable nouns. You cannot drop the article in front of a profession or title. So een technicus corresponds to English “a technician,” and zero-article constructions (like headlines in English) aren’t allowed in standard Dutch sentences.

How is the past tense repareerde formed from repareren?

repareren is a regular (weak) verb. To form the past tense:

Remove -en → stem repareer
Check the final consonant (r) against the 't kofschip rule: since r is not one of the voiceless consonants (t, k, f, s, ch, p), you add -de rather than -te.
You end up with repareerde. The extra e between stem and ending makes pronunciation smoother.

Could we also write Een technicus repareerde gelukkig het alarm nog dezelfde avond? Does changing the word order affect the meaning?

Yes. By starting with the subject you still respect V2 (subject + repareerde), and gelukkig moves into the mid-field. The overall meaning remains the same, but fronting Gelukkig (as in the original sentence) places extra emphasis on the speaker’s relief right at the start.