Learn Hardcore Swedish: Hon är nyfiken på vad som kan hända om hon byter jobb. - She is curious about what can happen if she changes job.

Using om here would sound wrong to a native speaker. Prepositions after adjectives are mostly fixed combinations you just have to learn, similar to English patterns like:

interested in (not interested on)
good at (not good in in this sense)

So you say:

Hon är nyfiken på X – She is curious about X.

Never nyfiken om X in this meaning.

Why is it vad som kan hända and not vad kan hända?

Vad kan hända? is a direct question:

Vad kan hända? – What can happen?

In the sentence you gave, this idea is embedded inside another clause (hon är nyfiken på …), so it becomes an indirect question:

Hon är nyfiken på vad som kan hända …
– She is curious about what can happen …

In Swedish, in an indirect question:

You still use a question word (vad, varför, hur, etc.).
But the word order becomes subject–verb, like a normal statement, not verb–subject as in a direct question.

So:

Direct: Vad kan hända? (question word + verb + subject)
Indirect: … vad som kan hända (question word + som
- verb)

What does som do in vad som kan hända? Is it really necessary?

Here som is a kind of “filler subject” / connector.

In English, what can function as the subject in what can happen.
In Swedish, that “what” is split into:

vad – the question word (“what”)
som – a pronoun/connector that stands for “the thing that …”

So vad som kan hända is literally like saying “what (it is that) can happen”.

It’s necessary here; vad kan hända after nyfiken på would sound like a direct question glued on, not a proper embedded clause.

Other similar patterns:

Jag undrar vad som händer. – I wonder what is happening.
Han vet inte vem som kommer. – He doesn’t know who is coming.

Why is there no question mark even though we have vad (“what”)?

There’s no question mark because this is not a direct question. It’s a statement that contains an indirect question:

Hon är nyfiken på [vad som kan hända om hon byter jobb].

The main clause (Hon är nyfiken på …) is a statement, so the whole sentence uses statement punctuation (a period).

Compare:

Direct question: Vad kan hända om hon byter jobb?
→ Ends with ?
Statement with indirect question:
Hon är nyfiken på vad som kan hända om hon byter jobb.
→ Ends with .

What is the exact role of om here? Does it mean “if” or “about/whether”?

In this sentence, om means “if”:

… vad som kan hända om hon byter jobb.
– what can happen if she changes jobs.

om can mean several things in Swedish:

if
- Om det regnar, stannar vi hemma. – If it rains, we stay home.
whether / if (in indirect questions)
- Jag undrar om han kommer. – I wonder whether/if he is coming.
Other meanings like about / concerning, around, etc., in different expressions.

Here it clearly introduces a condition (if she changes jobs), so it’s the “if” meaning.

Why is it byter jobb and not something like byter arbete or with an article like byter ett jobb?

A few points here:

Verb form
byta (to change) → present tense byter (she changes).
Swedish present tense just adds -r (or -er) for most verbs and is the same for all persons:
- jag byter, du byter, hon byter, etc.
jobb vs arbete
Both can mean “work” or “job”, but:
- jobb is more everyday / colloquial for “job/position”.
- arbete is more formal or more like “work” in general. So byta jobb = change job / change jobs (i.e. change position/employer).
Why no article (ett)? Phrases like byta jobb, få jobb, söka jobb often use jobb in the indefinite, article-less form when you’re talking about a job in a general or abstract sense, not one specific job.

So:

hon byter jobb ≈ she changes jobs / she changes job.
Saying byter ett jobb would sound odd here.

Why is it kan hända and not just händer?

kan is the modal verb “can”, and here it expresses possibility:

vad som kan hända – what can happen / what might happen

If you said vad som händer, it would mean:

vad som händer – what is happening / what happens (typically)

So the meanings differ:

vad som kan hända → focus on possible outcomes in the future
vad som händer → focus on what actually happens / is happening

In this sentence, she is curious about potential future scenarios, so kan hända is natural.

Why is byter in the present tense if we’re talking about a possible future job change?

Swedish very often uses the present tense for future time, especially in if-clauses and in other subordinate clauses:

Om hon byter jobb – If she changes jobs (in the future)
När jag kommer hem äter jag. – When I get home, I’ll eat.

You could use ska byta (is going to change) to emphasize the future a bit more:

… vad som kan hända om hon ska byta jobb.

But that sounds more like the decision is already made.
With plain byter, it’s neutral and common for a hypothetical future: “if she (were to) change jobs”.

Why is the subject hon repeated? Could you leave out the second hon in om hon byter jobb?

Swedish almost never drops the subject pronoun.
Each clause normally needs its own subject, even if it’s the same person:

Hon är nyfiken på … om hon byter jobb.

Leaving out the second hon (… om byter jobb) would be ungrammatical.

Compare:

Hon säger att hon är trött. – She says that she is tired.
(Both clauses need hon.)

Unlike some languages (like Spanish or Italian), Swedish is not a “pro‑drop” language; you generally keep the subject pronoun in every finite clause.

Does nyfiken change form for gender or number, like “curious” vs “curiosa” or something?

No. In this position, nyfiken is a predicative adjective, and it does not change form for gender or number:

Hon är nyfiken. – She is curious.
Han är nyfiken. – He is curious.
De är nyfikna. – They are curious.

The only change you often see is in the plural: nyfikna when the adjective goes with a plural noun or plural subject in certain positions:

nyfikna barn – curious children
Barnen är nyfikna. – The children are curious.

Here, with a singular subject hon, you simply use nyfiken.