På den ene siden mødrekvoten; på den andre siden medmorkvoten.

It is a fixed contrast pattern meaning on the one side ... on the other side, often very close to English on the one hand ... on the other hand.

In this example, it is not really making a full argument; it is just setting up a contrast between two categories:

• mødrekvoten
• medmorkvoten

So the structure is doing the job of framing two opposing or parallel items.

Because the noun side is part of a definite phrase here.

The pattern is:

• den ene siden
• den andre siden

In Norwegian, when an adjective comes before a definite noun, you usually get:

• a definite article like den
• the adjective in its definite/weak form
• the noun in definite form

So this is a standard definite noun phrase:

• den ene siden
• den andre siden

It is best to learn den ene ... den andre ... as a set expression.

Because side is in the definite singular.

The basic forms are:

• en side = a side
• siden = the side

So:

• på den ene siden = on the one side
• på den andre siden = on the other side

This definite form is the normal one in this expression.

Not really. It is an elliptical expression, meaning some words are left out because they are understood from context.

A fuller version could be something like:

• På den ene siden har vi mødrekvoten; på den andre siden har vi medmorkvoten.

Norwegian does this quite often in:

• headings
• lists
• labels
• short contrasts in formal writing

So the original is natural even without a verb.

They are both compound nouns, which are very common in Norwegian.

They break down like this:

• mødre + kvote + n → mødrekvoten
• medmor + kvote + n → medmorkvoten

The last part, kvote, is the main noun, and the final -n marks the definite singular.

So:

• mødrekvote = mother quota / mothers’ quota
• mødrekvoten = the mother quota
• medmorkvote = co-mother quota
• medmorkvoten = the co-mother quota

Because Norwegian compounds do not always use the bare singular noun as the first part. Very often, the first element appears in a special compound form, and sometimes that looks like a plural form.

Here, the established word is mødrekvote, with mødre-.

That makes sense semantically too: it refers to a quota connected with mothers as a group/category, not one individual mother.

So this is something you should mostly learn as a vocabulary item:

• mødrekvote
• fedrekvote
• foreldrepermisjon and so on

Medmor is a legal and family-related term meaning a co-mother: a female parent who is not the birth mother, often in contexts involving two mothers.

So medmorkvoten refers to a quota reserved for the medmor.

It is a specific social/legal term, not just a random compound.

The semicolon separates two parallel parts and makes the contrast clearer.

It works well here because the sentence has two balanced halves:

• På den ene siden mødrekvoten
• på den andre siden medmorkvoten

A semicolon is stronger than a comma, but weaker than a full stop. It is often used when two closely connected parts are being compared or contrasted.

Yes, in many varieties of Bokmål, that is possible.

The noun side can often appear with either:

• definite -en → siden
• definite -a → sida

So both of these can be seen:

• på den ene siden
• på den ene sida

The version in your sentence, siden, is completely standard and very common.

The hardest sound for many English speakers is ø.

A rough guide:

• mødre starts with a vowel somewhat like the vowel in British English bird, but with rounded lips
• mødrekvoten has main stress on the first syllable: MØ-dre-kvo-ten
• medmorkvoten also starts with main stress on the first syllable: MED-mor-kvo-ten

Also:

• kv in kvoten is pronounced with both sounds, roughly kv
• ene in den ene is roughly EH-neh
• andre is roughly AHN-dreh

These are only approximations, but they can help you get started.