Learn Hardcore Dutch: Hun grootste prioriteit is nu om veilig thuis te komen. - Their biggest priority now is to arrive home safely.

Yes. In Dutch, hun is the possessive pronoun corresponding to zij (they), so hun grootste prioriteit literally means their biggest priority.
Note that hun can also appear colloquially as an object pronoun (Ik zie hun), but the standard object form is hen. In this sentence, however, hun is correctly used to show possession.

How does the om ... te construction work in this sentence?

The om … te construction introduces a purpose or intention, much like English to in to get home safely. Its structure is:
• om (introduces the infinitive clause)
• any adverbs or objects (here veilig thuis)
• te
• the main verb at the end (here komen)
So om veilig thuis te komen = to get home safely.

Why does the verb komen go to the very end of the clause?

Dutch subordinate and infinitival clauses follow the “verb-at-the-end” rule. Even though om-clauses aren’t full subordinate clauses, they still push the mainverb to the end. That’s why you see om … te komen, with komen in final position.

Why is nu placed between is and om? Can its position change?

Nu is an adverb of time. In a Dutch main clause, adverbs typically come right after the finite verb (is). Hence is nu om …. You could also say:
• Hun grootste prioriteit is om nu veilig thuis te komen.
Both are correct, but the emphasis shifts:
– is nu om → now the priority exists
– om nu veilig → now the coming-home is the priority

Is thuiskomen always one word? Why is it split up here?

As a bare infinitive, you’d normally write thuiskomen (one word). But when you insert te before the main verb, you separate the adverb thuis and put te right before komen:
• om veilig thuis te komen
Think of thuis as an adverb of place, not a prefix, so it stays separate when te intervenes.

Can we omit om here and just say Hun grootste prioriteit is nu veilig thuis komen?

No. When you use an infinitive clause to express purpose or as a complement (after is, blijven, proberen, etc.), standard Dutch requires om … te. Dropping om would be ungrammatical in standard usage.

How is the superlative grootste formed from groot?

Dutch forms superlatives by adding -ste to the adjective root. For groot (big):
• Positive: groot
• Comparative: groter
• Superlative: grootste
Since it stands before a noun (prioriteit), you keep the extra e: grootste prioriteit.

What kind of word is prioriteit, and how do you pronounce it?

Prioriteit is a feminine noun borrowed from Latin/French. Plural: prioriteiten.
Pronunciation tips:
• Stress on the second syllable: prio-ri-teit
• The -iteit ending sounds like English -ity (e.g. prior-ITY).