Jeg må skynde mig, hvis jeg vil komme til tiden.

In this sentence, må means must / have to, not may.

That is a very common point of confusion for English speakers. Danish må can sometimes be related to permission, but in sentences like this one it usually expresses necessity:

• Jeg må skynde mig = I must hurry
• Du må gå nu can mean You may go now or You must go now, depending on context

So here, må is best understood as a modal verb showing necessity.

Because at skynde sig is a reflexive verb in Danish.

That means the verb normally goes together with a reflexive pronoun:

• jeg skynder mig = I hurry
• du skynder dig = you hurry
• han skynder sig = he hurries

So mig is not optional here. Danish says, literally, something like I hurry myself, even though English simply says I hurry or I hurry up.

Mig is the object/reflexive form of jeg.

Here is the pair:

• jeg = I
• mig = me

Since at skynde sig is reflexive, the subject jeg needs the matching reflexive/object form mig:

• Jeg skynder mig
• not Jeg skynder jeg

So mig is there because the verb requires it.

Because after modal verbs such as må, kan, skal, vil, and bør, Danish normally uses the bare infinitive.

So you get:

• jeg må komme
• jeg vil komme
• jeg kan komme

not:

• jeg må at komme
• jeg vil at komme

In this sentence, vil komme is completely normal because vil is a modal verb here.

It can be a little tricky, because Danish vil can mean either:

• want to
• or sometimes something close to will

In hvis jeg vil komme til tiden, the most natural reading is if I want to arrive on time or if I intend to arrive on time.

So here vil is about desire/intention, not just simple future.

Because the sentence has two clauses, and each clause needs its own subject.

The two parts are:

• Jeg må skynde mig
• hvis jeg vil komme til tiden

Even though both clauses refer to the same person, Danish still needs jeg in both places. English works the same way:

• I must hurry if I want to be on time

You cannot leave out the second jeg.

Because hvis introduces a subordinate clause, and Danish subordinate clauses normally keep the order subject + verb.

So:

• hvis jeg vil komme til tiden

is correct.

A native English speaker may expect inversion after if, but Danish does not invert the subject and verb just because the clause starts with hvis.

Compare:

• main clause: Jeg må skynde mig
• subordinate clause: hvis jeg vil komme til tiden

Til tiden means on time.

It is a fixed expression used for being punctual or arriving at the expected time:

• Han kom til tiden = He arrived on time
• Vi skal være der til tiden = We need to be there on time

So komme til tiden means arrive on time.

This is a very useful distinction.

• til tiden = on time, at the scheduled or expected time
• i tide = in time, before it is too late

Examples:

• Toget kom til tiden = The train arrived on time
• Vi nåede frem i tide = We arrived in time

So in your sentence, til tiden is used because the idea is punctuality, not just avoiding being too late by a narrow margin.

Because Danish usually puts a comma before a subordinate clause.

So in:

• Jeg må skynde mig, hvis jeg vil komme til tiden.

the comma marks the beginning of the hvis-clause.

This is different from English, where you would normally write:

• I must hurry if I want to be on time.

without a comma.

Yes, absolutely. That is a perfectly good sentence.

It means the same thing, but the order changes because the hvis-clause comes first. When a subordinate clause is placed first, the main clause shows inversion:

• Hvis jeg vil komme til tiden, må jeg skynde mig

Notice that it is må jeg, not jeg må, after the fronted clause.

So both are correct:

• Jeg må skynde mig, hvis jeg vil komme til tiden
• Hvis jeg vil komme til tiden, må jeg skynde mig

Yes, you could, but the nuance changes slightly.

• Jeg må skynde mig = I must / have to hurry
• Jeg skal skynde mig = I need to hurry / I am supposed to hurry

In many everyday situations, they can be quite close. But må often feels more like necessity from the situation, while skal can feel more like obligation, plan, or requirement.

So the original sentence sounds very natural for I need to hurry because of the time pressure.