Learn Swedish: Varför hade de ställt in bokningen? - Why had they cancelled the booking?

We use the past tense auxiliary verb hade (had) followed by the supine form of the main verb, which is ställt here. This works just like the English "had" + past participle to talk about an action that was completed before another event in the past.

Why are we using ställt in to mean "cancelled"? Doesn't ställa mean "to put" or "set"?

Yes, on its own, ställa means "to put" or "to set". But ställa in is a phrasal verb (a verb combined with a small particle word) that specifically means "to cancel". In Swedish, adding a particle like in often completely changes the verb's meaning!

Why are hade and ställt in separated by de?

This happens because of the V2 (verb-second) rule. In a question that starts with a question word like varför (why), the first verb (hade) must take the second position. The subject (de) is pushed to the spot immediately after it, and only then do we see the second verb (ställt).

Why does bokningen end in -en?