Hennes mamma visade henne hur man syr med nål och tråd när en knapp lossnar.

They are two different forms of she/her:

• hennes = her as a possessive, as in her mother
• henne = her as an object, as in showed her

So:

• Hennes mamma = her mother
• visade henne = showed her

English uses her for both, but Swedish keeps them separate.

Here man means one / you / people in general. It is the common Swedish way to talk about a general procedure.

So hur man syr means something like:

• how to sew
• how one sews
• how you sew

In English, we often use how to sew, but Swedish very often uses hur man + verb for this kind of general explanation.

Because hur man syr is an embedded question, not a direct question.

Compare:

• Direct question: Hur syr man? = How do you sew?
• Embedded question: Hon visade henne hur man syr. = She showed her how to sew.

In Swedish, embedded questions usually keep normal statement word order, so the subject comes before the verb:

• man syr
• not syr man

This is a very common pattern in Swedish.

Because the sentence mixes:

• a past event: visade = showed
• a general fact or general method: hur man syr / när en knapp lossnar

The mother showed her a general skill, not just what to do in one single moment. So Swedish uses the present tense for the general action:

• hur man syr = how you sew
• när en knapp lossnar = when a button comes off / comes loose

This is very natural in both Swedish and English when describing instructions or general truths.

Lossnar comes from lossna, which means to come loose, to loosen, or in this context to come off.

So när en knapp lossnar means:

• when a button comes loose
• when a button comes off

It does not necessarily mean the button completely falls to the floor; it means it is no longer properly attached.

This is a common Swedish pattern when talking about tools or materials in a general way.

• med nål och tråd = with needle and thread

Swedish often leaves out the article in fixed expressions like this when the meaning is general, not about one specific needle and one specific thread.

You could think of it as naming the method or equipment rather than counting individual objects.

Yes, absolutely. That would also be natural.

There is a small nuance:

• visade henne hur man syr = showed her how to sew
  This focuses on demonstrating the method.
• lärde henne att sy = taught her to sew
  This focuses more on teaching the skill.

So the original sentence suggests a practical demonstration, which fits very well with showed.

Because sin/sitt/sina refers back to the subject of the clause.

In this sentence, the subject is Hennes mamma. The possessive is not referring back to mamma; it refers to some other female person, the girl/woman being talked about.

So:

• hennes mamma = her mother
• sin mamma would mean his/her own mother, referring back to the subject

Using sin mamma here would change the reference and sound wrong in this context.

Syr is the present tense of sy, which means to sew.

Some useful forms are:

• infinitive: sy
• present: syr
• past: sydde
• supine: sytt

The present form syr may look unusual at first, so it is worth memorizing.

In this sentence, it most naturally has a general meaning:

• when a button comes off
• whenever a button comes loose

It describes the situation in which the skill is useful. The mother showed her how to do this kind of repair in that kind of situation.

If the speaker wanted to make it sound more clearly like one single past occasion, Swedish would probably phrase it differently.