Learn Icelandic: Tekur þú dótið þeirra? - Are you taking their stuff?

When you place a possessive word like þeirra after a noun, that noun usually must have the definite article attached to it. Dót means "stuff", and dótið means "the stuff". So in Icelandic, you literally say "the stuff their".

Does the word "þeirra" change if it owns a plural or feminine word?

No. Þeirra (their) is an invariable possessive word, just like hans (his) and hennar (her). That means it never changes its ending to match the gender, number, or case of the noun it owns. It is always just þeirra.

Why does the sentence begin with the verb "Tekur"?

In Icelandic, yes/no questions are made by putting the verb first. While English adds helper words like "Are" or "Do" (Are you taking...?), Icelandic simply swaps the subject and verb: Þú tekur (You take) becomes Tekur þú? (Are you taking?).

What case is the word "dótið" in here?

It is in the accusative case because it is the direct object being taken. Dót is a neuter word, and neuter words conveniently have the exact same spelling in both the nominative (subject) and accusative (object) cases.