Moju prijateljicu danas boli glava.

Because in this Serbian pattern with boleti (to hurt), the person who feels the pain is put in the accusative, not the nominative.

So here:

• moja prijateljica = nominative, the basic dictionary form
• moju prijateljicu = accusative, the person affected by the pain

Serbian is structuring this more like The head hurts my friend than My friend has a headache.

Because glava is the grammatical subject of the sentence: it is the thing that hurts.

So the structure is:

• moju prijateljicu = the person experiencing pain
• glava = the thing that hurts

That is why glava stays in the nominative.

The verb agrees with glava, not with moju prijateljicu.

Since glava is singular, the verb is singular too: boli.

Compare:

• Moju prijateljicu boli glava. = glava is singular
• Moju prijateljicu bole oči. = oči is plural, so the verb becomes bole

Very literally, it is something like:

My female friend today hurts head.

A more natural English explanation of the grammar would be:

Today, my female friend is hurt by her head or Today, my female friend’s head hurts.

So Serbian often uses a hurt structure where English often prefers have a headache.

Yes. Prijateljica means female friend, and prijatelj means male friend.

So this sentence specifically refers to a female friend.

If it were a male friend, you would say:

Mog prijatelja danas boli glava.

Because moja prijateljica is nominative, and that would make my friend the grammatical subject.

For the intended meaning, my friend is not the subject; the head is.

So for My female friend has a headache, Serbian needs:

Moju prijateljicu danas boli glava.

Using moja prijateljica would not express the same structure and would sound wrong for this meaning.

No. Serbian word order is fairly flexible.

You can also say:

• Danas moju prijateljicu boli glava.
• Moju prijateljicu boli glava danas.

The meaning stays basically the same, but the emphasis changes a little.

Starting with moju prijateljicu can highlight who is affected. Starting with danas can highlight when.

Yes, it is a very normal and common way.

Serbian often says:

• Boli me glava. = I have a headache
• Boli ga glava. = He has a headache
• Boli je glava. = She has a headache

You can also use a noun:

Moja prijateljica danas ima glavobolju.

That also means My friend has a headache today. Both are natural.

Yes. This is a very common Serbian pattern.

For example:

• Boli me stomak. = My stomach hurts / I have a stomachache
• Boli je ruka. = Her arm hurts
• Bole ga leđa. = His back hurts
• Bole me oči. = My eyes hurt

So the same idea appears again and again: the body part is the grammatical subject, and the person feeling the pain is in the accusative.

Then Serbian usually uses a short clitic pronoun:

• Boli je glava. = Her head hurts / She has a headache
• Danas je boli glava. = Today her head hurts

Here je means her in the accusative. It is not the verb is.

This is a very common pattern in Serbian, and learners often notice that these short pronouns tend to stand near the beginning of the sentence.