Learn Icelandic: Kennarinn fær svarið strax. - The teacher gets the answer immediately.

This is because fá is a strong verb. In the present tense, strong verbs often change their core vowel when used with singular subjects (I, you, he/she/it). For this verb, the vowel á shifts to æ, making the third-person singular form fær (gets). If the subject were plural, it would keep the original vowel (for example, við fáum).

Is svarið in the accusative case here since it is the object the teacher is getting?

Yes! The verb fá requires its object to be in the accusative case. However, svar (answer) is a neuter noun. A very helpful rule in Icelandic is that all neuter nouns look exactly the same in the accusative case as they do in the nominative (subject) case. So, svarið (the answer) doesn't change its spelling.

Both kennarinn (the teacher) and svarið (the answer) have "the" attached to them, but their endings are different. Why is that?

Icelandic definite articles (which mean "the") change depending on the gender of the noun. Kennari is a masculine noun ending in a vowel, so it just adds -nn to become kennarinn. Svar is a neuter noun ending in a consonant, so it adds -ið to become svarið.

Where does the adverb strax (immediately) go in a simple Icelandic sentence?