Hon skakar på huvudet när hon inte håller med.

In Swedish, skaka på huvudet is the normal expression for to shake your head.

The på is part of the idiomatic phrase. Swedish often uses a preposition in places where English does not. So even though English says shake her head, Swedish says shake on the head, literally.

So:

• Hon skakar på huvudet = She shakes her head

If you leave out på, it sounds unnatural in this meaning.

Swedish often uses the definite form for body parts when it is obvious whose body part is meant.

So instead of saying:

• hon skakar sitt huvud

Swedish normally says:

• hon skakar på huvudet

This is very common with body parts and clothing when the owner is clear from the context.

Examples:

• Han tvättar händerna = He washes his hands
• Hon stänger ögonen = She closes her eyes

So huvudet here means the head, but in natural English we translate it as her head.

Hålla med is a fixed expression meaning to agree.

Literally, hålla usually means hold, and med means with, but together hålla med does not mean hold with in a literal physical sense. It is just the Swedish verb phrase for agree.

Examples:

• Jag håller med = I agree
• Hon håller inte med = She does not agree

So in your sentence:

• när hon inte håller med = when she does not agree

Because hålla med is a complete verb phrase on its own.

You can say:

• Jag håller med = I agree

If you want, you can also add who or what you agree with:

• Jag håller med dig = I agree with you
• Hon håller med läraren = She agrees with the teacher

But the object does not have to be stated if it is already understood from the context.

This is because när hon inte håller med is a subordinate clause.

In Swedish subordinate clauses, sentence adverbs such as inte usually come before the finite verb.

So:

• Main clause: Hon håller inte med
• Subordinate clause: ... när hon inte håller med

This is a very important word-order pattern in Swedish.

A useful rule is:

• In main clauses, inte usually comes after the finite verb
• In subordinate clauses, inte usually comes before the finite verb

Normally, Swedish repeats the subject in each clause.

So:

• Hon skakar på huvudet när hon inte håller med

is natural, because each clause has its own subject:

• Hon skakar på huvudet
• när hon inte håller med

Leaving out the second hon would sound incomplete or incorrect in standard Swedish.

Here när means when, and often in English it can also feel like whenever.

So the idea is:

• She shakes her head when she does not agree
• She shakes her head whenever she does not agree

It describes what happens in that situation.

If you wanted a more hypothetical meaning, English might use if, and Swedish would more often use om.

Compare:

• När hon inte håller med, skakar hon på huvudet = When/whenever she does not agree, she shakes her head
• Om hon inte håller med, kommer hon att säga det = If she does not agree, she will say so

Both are in the present tense.

• skakar = shakes / is shaking
• håller = agrees / is agreeing, depending on context, though in English agree is usually not used in the progressive

The dictionary forms are:

• skaka = to shake
• hålla med = to agree

Swedish present tense often ends in -r:

• skaka → skakar
• hålla → håller

It can be understood as a general habit or repeated behavior.

• Hon skakar på huvudet när hon inte håller med

most naturally means something like:

• She shakes her head when she does not agree
• She tends to shake her head when she disagrees

Without extra context, it sounds more like a general statement than one single event.

Yes. Hålla med can be used both on its own and with a person or statement.

Examples:

• Jag håller med = I agree
• Jag håller med dig = I agree with you
• Vi håller med läraren = We agree with the teacher

In your sentence, the person or idea she disagrees with is not stated, because it is either obvious or unimportant.

No, not in this meaning.

Hålla med sig would mean something like agree with oneself, which is not what is meant here.

For ordinary agree/disagree, you usually say:

• hålla med = agree
• inte hålla med = disagree / not agree

If you want to mention the person, you add it directly:

• hon håller med honom = she agrees with him
• hon håller inte med dem = she does not agree with them

Yes, that is also correct.

It just puts the time/condition clause first:

• När hon inte håller med, skakar hon på huvudet

When a subordinate clause comes first in Swedish, the main clause follows normal verb-second word order, so you get:

• ..., skakar hon på huvudet not
• ..., hon skakar på huvudet

Both versions are correct:

• Hon skakar på huvudet när hon inte håller med
• När hon inte håller med, skakar hon på huvudet

The meaning is basically the same.