Learn Hardcore Norwegian: Sjefen spør de ansatte om de kan fortsette prosjektet. - The boss asks the employees if they can continue the project.

sjefen means the boss. The root sjef means boss, and adding -en is the definite singular ending in Bokmål, turning sjef (a boss) into sjefen (the boss).

Why is it de ansatte and not just ansatte, or dem ansatte?

de ansatte means the employees.

ansatte (indefinite plural) means employees.
de is the plural definite article, making de ansatte = the employees.
You can’t say dem ansatte because dem is the object form of the pronoun “they” and can’t serve as an article. If you wanted indefinite you’d just say ansatte.

What is the role of om in this sentence? How is it different from hvis?

In this context, om is a subordinating conjunction meaning whether or if (in indirect questions). It introduces the embedded question “whether they can continue the project.”
hvis also means if but is used for real or hypothetical conditions (“if this happens…”), not for indirect questions.

What is the infinitive of spør, and why is the present tense just spør?

The infinitive is å spørre (to ask). In the present tense (both singular and plural) it’s spør:

jeg spør (I ask)
du spør (you ask)
han/hun spør (he/she asks)
vi/de spør (we/they ask)

Why is there no comma before om?

Norwegian often omits commas before subordinate conjunctions like om or at. Unlike English, a comma isn’t required here. You might add one for clarity in very long sentences, but in this short sentence it’s normal to leave it out.

What does prosjektet mean, and why is it in the definite form?

prosjektet means the project.

prosjekt = a project (indefinite)
prosjektet = the project (definite singular)
Since we’re talking about a specific project, the definite form is used.

Why is fortsette in the infinitive form instead of fortsetter?

After a modal verb like kan (can), Norwegian uses the bare infinitive of the next verb (without å). So it’s kan fortsette rather than kan fortsetter.
If you wanted to express “they continue” without a modal, you’d say de fortsetter prosjektet.

What is the word order in the subordinate clause om de kan fortsette prosjektet?

In subordinate clauses introduced by a conjunction (like om), Norwegian follows Subject–Verb–Object:

de (subject)
kan (verb)
fortsette prosjektet (object)
The conjunction om doesn’t count toward the verb-second (V2) rule, so the verb stays right after the subject.

Could de in om de kan fortsette prosjektet be the formal you?

The formal “you” in Bokmål is also spelled De but always capitalized. Here it’s lowercase de, so it’s the third-person plural pronoun meaning they, referring back to de ansatte.