Learn Icelandic: Amman smurði okkur alltaf brauðið. - The grandma always buttered the bread for us.

This is a classic example of the "dative of advantage." In Icelandic, instead of using a preposition to say you did an action for someone's benefit, you can often just put the person benefiting into the dative case (like okkur) right after the verb. Saying smurði okkur sounds much more natural to native speakers than using fyrir in this context.

Why does the adverb alltaf come right in the middle of the two objects?

This follows a specific word-order rule in Icelandic. When you have a short pronoun acting as an indirect object (okkur) and a full noun acting as a direct object (brauðið), a sentence adverb like alltaf usually slips right between them. The standard flow is: Verb -> Pronoun Object -> Adverb -> Noun Object.

I know the infinitive is smyrja (to butter/smear). Why does the past tense change to smurði with a "u"?

Smyrja is a weak verb, but it belongs to a sub-class that experiences a vowel shift in the past tense. The y in the stem shifts to a u before the past tense suffix -rði. You might recognize this exact same pattern from the very common verb spyrja (to ask), which becomes spurði in the past.

Does the verb smyrja only apply to food, or can it mean other types of spreading/smearing?