Learn Icelandic: Amma var mjög hissa áðan. - Grandma was very surprised earlier.

Var is the past tense of vera (to be) for the third-person singular (he, she, or it). Because the subject is Amma (Grandma), which is a "she", we use var. Notice that it's exactly the same word you would use for "I was" (ég var).

I thought adjectives had to match the gender of the noun. Why doesn't hissa have a feminine ending to match Amma?

Most adjectives do change to match the noun, but hissa (surprised) is a special exception. It is an indeclinable adjective, which means its spelling never changes. Whether it's a man, a woman, or a large group of people who are surprised, the word remains exactly the same: hissa.

What exact timeframe does áðan refer to?

Áðan translates to "earlier" or "just now" in the sense of the very recent past. You use it to talk about something that happened a few minutes or a few hours ago, but always on the exact same day.

Is mjög always placed right before the adjective?

Yes! Just like the word "very" in English, the adverb mjög goes directly in front of the adjective it describes (in this case, making it mjög hissa).