På den ene siden utsettelse; på den andre siden endringssøknad.

Not really. It is more like an elliptical or headline-style sentence fragment.

A fuller version might be something like:

• På den ene siden er det utsettelse; på den andre siden en endringssøknad.
• På den ene siden handler det om utsettelse; på den andre siden om endringssøknad.

The original sounds natural in notes, headings, summaries, or bureaucratic writing, where Norwegian often leaves out words that are understood from context.

It is a fixed contrasting pattern meaning on the one hand ... on the other hand ....

It sets up two opposing or contrasting sides of an issue.

Structure:

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

Even though it literally contains side, you should usually learn it as one expression.

Because Norwegian uses den ene ... den andre ... when referring to one of two and the other one.

So:

• den ene = the one / one of the two
• den andre = the other

In this phrase, the idea is literally the one side versus the other side.

Using just en or annen would not sound right in this fixed expression.

Here, siden is the definite form of the noun side:

• 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 is different from siden meaning since or later/afterwards. Context makes it clear.

Because this is compressed, note-like language.

The nouns are being presented almost like labels or categories, not as fully built noun phrases. That is why you do not see:

• en utsettelse
• en endringssøknad

In a fuller sentence, you might well add an article, especially with endringssøknad, which is clearly countable:

• På den ene siden er det snakk om utsettelse; på den andre siden en endringssøknad.

With utsettelse, article omission is especially natural because it can feel more abstract, like postponement in English.

Because Norwegian normally writes compound nouns as one word.

So:

• endring = change, amendment
• søknad = application

Together:

• endringssøknad = application for change / amendment application

This is very typical Norwegian spelling. English often separates these ideas into several words, but Norwegian usually combines them.

Then you need normal Norwegian V2 word order.

If you begin with På den ene siden, the verb usually comes next:

• På den ene siden er det utsettelse.
• På den andre siden er det en endringssøknad.

Notice that Norwegian does not keep English-style order such as På den ene siden det er ....
The finite verb must come early, in second position.

The semicolon separates two parallel contrasting parts:

• På den ene siden utsettelse
• på den andre siden endringssøknad

It works well because both halves are short, balanced fragments. A comma might be possible in looser writing, but the semicolon makes the contrast clearer and neater.

Yes. In Bokmål, side can have two definite singular forms:

• siden
• sida

So both are possible:

• på den ene siden
• på den ene sida

The version with siden is very common in standard written Bokmål. Sida can sound a bit more colloquial or dialect-friendly, depending on context.

Usually not in exactly this stripped-down form, unless they are reading from notes or speaking very formally.

In normal speech, people would often add more structure, for example:

• På den ene siden er det snakk om utsettelse, men på den andre siden må de sende en endringssøknad.
• På den ene siden ønsker de utsettelse; på den andre siden leverer de en endringssøknad.

So the original is understandable and natural in the right context, but it is more written, compressed, and administrative in tone than everyday conversation.