Hvis hendes mus stadig ikke reagerer ordentligt i morgen, vil hun købe en ny på vej hjem fra arbejdet.

Because Danish main clauses follow the V2 rule: the finite verb normally comes in the second position.

Here, the sentence begins with the if-clause:

Hvis hendes mus stadig ikke reagerer ordentligt i morgen

Since that whole clause takes the first position, the main clause must begin with the finite verb:

vil hun købe en ny ...

So the pattern is:

• [fronted element] + [finite verb] + [subject]

That is why you get:

• ..., vil hun købe ...

and not:

• ..., hun vil købe ...

Because Hvis hendes mus stadig ikke reagerer ordentligt i morgen is a subordinate clause, and subordinate clauses in Danish have different word order from main clauses.

In a main clause, Danish usually has the finite verb early because of the V2 rule.
In a subordinate clause, sentence adverbs like ikke often come before the finite verb.

So compare:

• Main clause: Musen reagerer ikke
• Subordinate clause: ... hvis musen ikke reagerer

In your sentence, that becomes:

• Hvis hendes mus stadig ikke reagerer ordentligt i morgen

where stadig ikke comes before reagerer.

Stadig ikke means still not.

• stadig = still
• ikke = not

So:

• stadig ikke reagerer = still doesn’t respond / still isn’t responding

Using both words shows that the problem is continuing. It is not just a simple negative; it means the mouse has already been failing to respond, and that may still be true tomorrow.

A learner might compare it with endnu ikke, which often means not yet.
Very roughly:

• stadig ikke = still not
• endnu ikke = not yet

They can overlap, but stadig ikke emphasizes continued non-functioning.

Because ordentligt is the adverb form, and here it modifies the verb reagerer.

• ordentlig = proper/properly functioning, as an adjective
• ordentligt = properly, correctly, as an adverb

In the sentence, the word describes how the mouse responds:

• reagerer ordentligt = responds properly

This -t ending is very common when turning an adjective into an adverb in Danish.

Yes. Mus can mean both:

• a mouse (the animal)
• a computer mouse

Just like in English, context tells you which one is meant.
In this sentence, because it says doesn’t respond properly and then talks about buying a new one, it is clearly a computer mouse.

Also, mus has the same form in singular and plural in many contexts, so the article or surrounding words help:

• en mus = a mouse
• hendes mus = her mouse

Here it is singular because the sentence is talking about one device.

Danish often leaves out a noun when it is already obvious from context.

So:

• købe en ny mus = buy a new mouse
• købe en ny = buy a new one

The noun mus is understood, so it does not need to be repeated.

The word en is used because mus is a common-gender noun:

• en mus
• therefore en ny

If the noun were a neuter noun, you would expect et nyt instead.

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

Here, i morgen already tells you the time is in the future, so Danish does not need a separate future form in the if-clause.

So:

• Hvis hendes mus ... reagerer ... i morgen
  means something like
• If her mouse still doesn’t respond properly tomorrow

This is very natural in Danish. English does something similar in many conditional sentences too:

• If it rains tomorrow, ... not
• If it will rain tomorrow, ...

So the Danish structure is quite normal.

It tells you when / under what circumstances she will buy the new mouse:

• på vej hjem = on the way home
• fra arbejdet = from work / from the workplace

So the idea is that she will buy it while she is on her way home from work.

This is a very natural Danish expression.
You can think of it as one chunk:

• på vej hjem = on the way home

Then fra arbejdet adds where she is coming from.

The definite form arbejdet literally means the work or the workplace/work situation in question.

In Danish, the definite form is often used where English would simply say work. So:

• fra arbejdet can correspond to English from work

This makes good sense if the speaker is thinking of her workplace / the place she is leaving.

You may also encounter fra arbejde in Danish, depending on style and nuance, but fra arbejdet is completely natural here.

Yes. Danish word order is fairly flexible with time expressions, especially for emphasis or style.

The version in your sentence:

• Hvis hendes mus stadig ikke reagerer ordentligt i morgen ...

is natural and clear.

But other placements can also be possible, for example:

• Hvis hendes mus i morgen stadig ikke reagerer ordentligt ...

That can sound slightly more focused on tomorrow.

So the placement of i morgen is not arbitrary, but it is also not fixed in just one position. The original sentence sounds smooth and idiomatic.

Because the sentence begins with a subordinate clause, and the comma marks the boundary before the main clause begins.

So the structure is:

• Hvis hendes mus stadig ikke reagerer ordentligt i morgen,
  vil hun købe en ny ...

The comma helps show where the if-clause ends and the main statement starts.

This is especially useful in Danish because the word order changes after that point:

• subordinate clause first
• then main clause with inversion: vil hun købe

So the comma is both grammatical and helpful for reading.