Learn Icelandic: Þau tala sænsku heima hjá sér.

Yes, you can! Heima alone means 'at home'. However, adding hjá sér (literally 'by themselves') is a very common, idiomatic way to specify 'at their place' or 'at their own home'.

Why do we use the reflexive pronoun sér here instead of þeim?

The reflexive pronoun sér always points back to the subject of the sentence, which is Þau. If you said heima hjá þeim, it would mean they are speaking Swedish at somebody else's home. Because it is their own home, we must use the reflexive form.

Why does the word for Swedish, sænska, change to sænsku here?

The verb tala (to speak) forces the language being spoken into the accusative case. Most languages in Icelandic are feminine nouns ending in -a, like sænska. In the accusative case, that -a changes to -u, giving us sænsku.

Does the pronoun Þau tell us anything about the people in the group?

Yes, it tells us the group is either mixed-gender or their genders are unknown. Þau is the neuter plural pronoun. If the group were all male, you would use Þeir, and if they were all female, you would use Þær.