Learn Icelandic: Þumallinn á þér er aumur, er það ekki?

For external body parts like a thumb, Icelandic typically uses the definite noun plus á and a dative pronoun to show who it belongs to. So instead of using a possessive pronoun like your thumb (þumallinn þinn), you literally say the thumb on you (þumallinn á þér). This is standard for things that are physically attached to the outside of your body.

Why is the adjective aumur (sore) in the masculine form here?

The adjective must agree with the noun it describes. Here, aumur is describing the thumb (þumallinn), which is a masculine noun. Even if you are talking to a woman, the thumb is still masculine, so the adjective stays in the masculine nominative singular form.

Is er það ekki? always used for tag questions like aren't you or doesn't she?

Yes! In English, we constantly change the tag depending on the sentence, such as doesn't he, aren't they, or hasn't she. In Icelandic, it is much easier: you can just use er það ekki? (literally is it not?) as a universal tag to ask for confirmation at the end of almost any statement.

What is the base form of þumallinn before adding the definite article?

The base dictionary form is þumall (a thumb). Because it is a masculine noun ending in -ll, you simply add the definite article -inn to the end to get þumallinn (the thumb).