Hvis jeg hoster i nat, bliver jeg hjemme i morgen.

Because Danish very often uses the present tense for the future when the time is clear from context.

Here, i nat and i morgen already show that the events are in the future, so hoster is natural.

• Hvis jeg hoster i nat = If I cough tonight
• bliver jeg hjemme i morgen = I’ll stay home tomorrow

This is similar to English sentences like If it rains tomorrow, I’m staying home, where present forms can also refer to the future.

This is because of normal Danish word order.

The sentence starts with the if-clause:

• Hvis jeg hoster i nat

After that comes the main clause, and in Danish main clauses the finite verb normally comes in second position. Since the if-clause is occupying the first position, the verb comes next:

• bliver
  • jeg

So:

• Hvis jeg hoster i nat, bliver jeg hjemme i morgen.

If the main clause stood alone, it would be:

• Jeg bliver hjemme i morgen.

This is a very important Danish pattern:

• Når det regner, bliver vi inde.
• Hvis du kommer, bliver jeg glad.

Yes, at blive often means to become, but it also has other common meanings.

In the expression blive hjemme, it means:

• stay home
• remain at home

So in this sentence, bliver jeg hjemme does not mean I become home. It means I stay home.

This is a fixed, very common use:

• Jeg bliver hjemme i dag. = I’m staying home today.
• Hun blev hjemme fra skole. = She stayed home from school.

Because Danish distinguishes between:

• hjem = homeward / to home (direction)
• hjemme = at home (location)

In this sentence, the meaning is staying at home, not going home, so hjemme is correct.

Compare:

• Jeg går hjem. = I’m going home.
  (movement toward home)

• Jeg er hjemme. = I’m at home.
  (location)

• Jeg bliver hjemme. = I stay home / stay at home.
  (remaining in that location)

Yes. You can say:

• Hvis jeg hoster i nat, så bliver jeg hjemme i morgen.

The så is often optional in sentences like this. It can make the result part feel a bit more explicit, like then in English.

So both are natural:

• Hvis jeg hoster i nat, bliver jeg hjemme i morgen.
• Hvis jeg hoster i nat, så bliver jeg hjemme i morgen.

Without så is very common, especially in neutral written Danish.

Here you need hvis, because this is a real condition:

• If I cough tonight, I’ll stay home tomorrow.

In Danish:

• hvis = if in conditional sentences
• om = often whether / if in indirect questions

So:

• Jeg ved ikke, om han kommer. = I don’t know if / whether he is coming.
• Hvis han kommer, bliver jeg glad. = If he comes, I’ll be happy.

In your sentence, hvis is the correct word.

Because these are fixed Danish time expressions.

• i morgen = tomorrow
• i nat = tonight / during the night

You usually just learn them as whole expressions.

A useful contrast is:

• i nat = one specific night, usually tonight or last night, depending on context
• om natten = at night in general / during the night habitually

So here:

• Hvis jeg hoster i nat...
  means If I cough tonight..., not If I cough at night in general...

Not always. It depends on context.

• When talking about the coming night, i nat often means tonight
• In other contexts, it can mean last night

But in this sentence, because the whole sentence is about a possible future result (tomorrow), i nat is naturally understood as tonight.

So the context makes the meaning clear.

Yes, in standard written Danish you normally put a comma after an initial subordinate clause like this:

• Hvis jeg hoster i nat, bliver jeg hjemme i morgen.

The part beginning with hvis is a subordinate clause, and it is followed by the main clause, so the comma marks that boundary.

This is a very common pattern:

• Hvis det regner, tager jeg bussen.
• Når du kommer hjem, ringer du til mig.

You could, but it changes the feel of the sentence a little, and the original version is more natural.

For example:

• Hvis jeg hoster i nat, vil jeg blive hjemme i morgen.

This is possible, but Danish often prefers the simple present with a time expression:

• Hvis jeg hoster i nat, bliver jeg hjemme i morgen.

Using vil can sometimes sound a bit more like a decision, intention, or prediction, while the plain present is very normal and straightforward in Danish.

So for a simple conditional statement, the original sentence is excellent Danish.