Learn Icelandic: Arfurinn er mjög mikill. - The inheritance is very large.

In Icelandic, stór is mainly used for physical size, like a large house or a tall person. For abstract quantities, amounts of money, or concepts like an inheritance (arfur), you use mikill to mean much, great, or large.

What gender is arfurinn, and how does it affect the adjective?

Arfurinn is a masculine noun (arfur) with the definite article (-inn) attached. Because it is masculine, singular, and in the nominative case as the subject of the sentence, the adjective describing it must match. That is why we use the masculine form mikill instead of the feminine mikil or neuter mikið.

Since this lesson covers proportions, how would you say "half of the inheritance"?

You would use the noun helmingur (a half) followed by the inheritance in the genitive (possessive) case. The genitive form of arfurinn is arfsins, so "half of the inheritance" is helmingur arfsins.

Does the word mjög need to agree with the noun like the adjective does?

No, mjög (very) is an adverb describing the degree of the adjective mikill. Unlike adjectives, adverbs do not change their endings to match the gender, number, or case of a noun. It is always just mjög.