Learn Hardcore Dutch: Mijn opdracht is kort, maar belangrijk.

Because the possessive pronoun mijn replaces the article. In Dutch you never use both a definite article and a possessive on the same noun (you don’t say de mijn opdracht).

Why is mijn not mijne?

Mijne is a standalone pronoun, used when you don’t mention the noun again (for example: Deze opdracht is de mijne). When you directly modify a noun, you use mijn.

Why don’t kort and belangrijk get an -e ending?

They are predicative adjectives here (they follow the verb is and describe the subject). Predicative adjectives in Dutch stay in their base form (no -e).

Could I write korte and belangrijke instead?

Only if they’re attributive, i.e. placed before the noun. Then you’d say mijn korte maar belangrijke opdracht and drop the verb is. Attributive adjectives get -e because opdracht is a de-word.

Is the comma before maar mandatory?

No. In a simple sentence like this the comma is optional. Writers often put it to signal a slight pause or to emphasize the contrast. Both
Mijn opdracht is kort maar belangrijk
and
Mijn opdracht is kort, maar belangrijk
are correct.

Can I use a different conjunction instead of maar?

For a direct contrast maar is the most common. In more formal or written Dutch you might see echter, but it typically comes at clause start or after a semicolon:
Mijn opdracht is kort; echter belangrijk.

How do I form the plural of opdracht, and do the adjectives change?

The plural is opdrachten. With plural you’d say
Mijn opdrachten zijn kort maar belangrijk.
The verb changes to zijn, but since the adjectives remain predicative, they still have no -e.

Could I invert the sentence to emphasize the adjectives?

Yes. You can front the adjectives for emphasis or a stylistic effect:
Kort maar belangrijk is mijn opdracht.
This inversion is grammatically correct but more poetic or marked than the normal S-V-O order.