Hvis min bror er syg, bliver han hjemme.

Because Danish follows the V2 rule in main clauses: the finite verb usually comes in the second position.

In this sentence, the if-clause Hvis min bror er syg comes first. That whole clause counts as position 1, so the main clause must begin with the verb:

• Hvis min bror er syg, bliver han hjemme.

If you start with the main clause instead, the word order is more like English:

• Han bliver hjemme, hvis min bror er syg.

So the unusual order is caused by Danish sentence structure, not by the meaning of if.

Hvis means if and introduces a subordinate clause.

So in:

• Hvis min bror er syg

the speaker is giving a condition. The main clause then tells what happens under that condition:

• bliver han hjemme

This is very similar to English if my brother is sick, he stays home.

In Danish, just like in English, syg is an adjective, so it is used with to be:

• han er syg = he is ill / sick

You do not use have here.

So:

• min bror er syg = my brother is sick

This works the same way with many adjectives:

• han er træt = he is tired
• hun er glad = she is happy

Bliver is the present tense of blive, which often means become, but it also has other uses.

In bliver hjemme, it means something like stays/remains at home.

So although blive often means become, in this expression:

• blive hjemme = stay home / stay at home

This is a very common fixed expression in Danish.

Because hjemme refers to a location: at home.

• han er hjemme = he is at home
• han bliver hjemme = he stays at home

By contrast, hjem usually expresses direction or movement toward home:

• han går hjem = he goes home

A useful shortcut is:

• hjemme = location
• hjem = direction

In Danish, possessive words like min, din, hans, vores normally come directly before the noun, without an article.

So:

• min bror = my brother

You do not add a separate definite ending or article here.

Compare:

• bror = brother
• min bror = my brother
• broren is not standard Danish in this meaning

This is different from some other Scandinavian patterns learners may have seen elsewhere.

Yes, Danish adjectives can change form, but syg is correct here because it agrees with a singular common-gender noun: bror.

Here are the main forms:

• en syg bror = a sick brother
• et sygt barn = a sick child
• syge børn = sick children
• den syge mand = the sick man

Since bror is a common-gender singular noun, the base form syg is the right one.

Yes, absolutely.

That version is also correct:

• Han bliver hjemme, hvis min bror er syg.

The difference is mainly word order and emphasis.

• Hvis min bror er syg, bliver han hjemme.
  This starts with the condition.
• Han bliver hjemme, hvis min bror er syg.
  This starts with the result.

Both mean the same thing. The first one is useful if you want to emphasize the condition first.

Yes, it can be.

Danish often uses the present tense for future meaning, especially when the context makes the time clear.

So:

• Hvis min bror er syg, bliver han hjemme.

can mean:

• If my brother is sick, he stays home
• If my brother is sick, he will stay home

English often uses will, but Danish very often just uses the present tense in this kind of sentence.

The comma separates the subordinate clause from the main clause:

• Hvis min bror er syg, bliver han hjemme.

This helps show the structure clearly:

• condition: Hvis min bror er syg
• result: bliver han hjemme

In Danish, commas are often used to mark clause boundaries like this. You may also notice some variation in comma style depending on writing conventions, but this comma is completely normal and helpful for learners.

A careful pronunciation would be approximately:

• Vis min bro er sy, bliver han hjemme

But that is only a rough guide for English speakers.

A few important points:

• Hvis often sounds close to vis
• bror has a Danish r sound that is not like a strong English r
• syg has a vowel sound English does not really have
• bliver is often pronounced more like bli-ver or even more reduced in natural speech
• hjemme begins with a y-like / j-like sound, roughly similar to the start of yes

If you want, the safest learning strategy is to focus first on:

• hvis
• syg
• hjemme

because those are the words whose pronunciation usually feels least familiar to English speakers.