Programmet starter nå.

Because programmet is the definite singular form: the program.

• et program = a program
• programmet = the program

Norwegian often adds the definite ending directly to the noun instead of using a separate word like the in English.

Since program is a neuter noun, the definite ending is -et.

Here, -et marks definite singular for a neuter noun.

So:

• et program = a program
• programmet = the program

This is very common in Norwegian. Compare:

• et hus = a house
• huset = the house

Starter is the present tense form of starte.

• å starte = to start
• starter = starts / is starting

In Norwegian, present tense verbs usually end in -r, and they do not change depending on the subject:

• jeg starter = I start / am starting
• du starter = you start
• programmet starter = the program starts

So Norwegian is simpler than English here: no special -s for he/she/it.

It can mean either, depending on context.

Programmet starter nå can naturally be understood as:

• The program starts now
• The program is starting now

Norwegian present tense often covers both the simple present and the present progressive that English distinguishes.

Nå means now, and putting it at the end is very natural in Norwegian:

• Programmet starter nå.

This is similar to English The program starts now.

But Norwegian also allows nå at the beginning:

• Nå starter programmet.

That version is also correct, but because Norwegian main clauses usually follow the verb-second (V2) rule, when nå comes first, the verb starter must come before the subject programmet.

So:

• Programmet starter nå.
• Nå starter programmet.

Both are correct.

Yes, absolutely.

Both starte and begynne can mean start / begin.

• Programmet starter nå.
• Programmet begynner nå.

Both are natural. In many contexts, they are interchangeable.
A small difference is that begynne is often felt as the more direct equivalent of begin, while starte can sound especially natural for things like shows, machines, events, or processes starting.

It depends on context.

Program in Norwegian can refer to several things, such as:

• a TV or radio program
• a computer program
• a schedule/program for an event

So Programmet starter nå could mean:

• The show starts now
• The program starts now
• The software is starting now

The surrounding context tells you which meaning is intended.

A simple learner-friendly guide would be:

• Programmet ≈ pro-GRAM-met
• starter ≈ STAR-ter
• nå has a long vowel, roughly like no but with a different Norwegian vowel quality

A few useful notes:

• The tt in starter is usually pronounced like a normal t sound.
• The å in nå is the Norwegian å sound, not the English a.
• In natural speech, the sentence is usually said smoothly, with stress often falling on gram in programmet and on nå if you want to emphasize now.

Yes. It follows the very common pattern:

subject + verb + time expression

• Programmet = subject
• starter = verb
• nå = time word

So it is a very standard, natural Norwegian sentence.

It is a good example of a simple declarative sentence in Norwegian.