Learn Icelandic: Stelpan kyssir pabba.

Pabba is the accusative form of pabbi. In Icelandic, the person or thing receiving the action (the direct object) takes the accusative case. Since Dad is the one being kissed, the word changes from the dictionary form pabbi to pabba.

How would I say "The girl kisses him" using the pronouns from this lesson?

You would replace pabba with the accusative pronoun for "him", which is hann. The sentence becomes Stelpan kyssir hann. Because the verb kyssa (to kiss) forces its object into the accusative case, you must use an accusative pronoun. Notice that for the masculine pronoun, the nominative (he) and accusative (him) forms are exactly the same: hann!

Where is the word for "the" in Stelpan?

In Icelandic, "the" isn't a separate word that goes before the noun. Instead, it is a suffix added to the end. The base word is stelpa (a girl), and adding -n makes it stelpan (the girl).

Why doesn't the sentence need a word for "her" before "Dad"?

Just like in English, Icelanders often treat close family words like pabbi (Dad) and mamma (Mom) almost like names, without needing possessive words like "her" or "his". Saying Stelpan kyssir pabba is the most common and natural way to say "The girl kisses her dad."