Konstabelen kommer snart.

Because Norwegian usually puts the definite article on the end of the noun.

• konstabel = a constable / constable
• konstabelen = the constable

So the -en here means the.

In English, you say the constable with a separate article. In Norwegian, the definite form is often built into the noun itself:

• en konstabel = a constable
• konstabelen = the constable

A separate word like den is usually added when there is an adjective:

• den gamle konstabelen = the old constable

So in this sentence, konstabelen by itself already means the constable.

Norwegian very often uses the present tense to talk about the near future, especially when a time word makes the meaning clear.

So:

• Konstabelen kommer snart. = The constable is coming soon / will come soon

This is completely natural in Norwegian.
You can also use other future expressions, such as skal komme, but the simple present is very common.

Snart means soon or in a little while.

In this sentence, it tells you that the action will happen before long:

• kommer snart = is coming soon

It does not mean early.
For early, Norwegian would usually use tidlig.

This sentence has very straightforward Norwegian word order:

• Konstabelen = subject
• kommer = verb
• snart = adverb

So it follows the common pattern:

subject + verb + adverb

That gives:

Konstabelen kommer snart.

Yes. That is also grammatical.

Norwegian is a V2 language, which means the verb normally comes in the second position in main clauses. So if you move snart to the front, the verb still stays second:

• Konstabelen kommer snart.
• Snart kommer konstabelen.

Both are correct. The second version gives a bit more emphasis to soon.

It is understandable, but it can sound a bit formal, old-fashioned, or tied to a specific rank or style of speech, depending on context.

In modern everyday Norwegian, people may more often use words like:

• politibetjent = police officer
• politimann = policeman (less neutral)

So konstabelen is fine to understand and use in some contexts, but it is not always the most everyday choice.

A rough guide is:

kon-sta-BE-len KOM-mer snart

A few helpful points:

• konstabelen has the stress on be
• kommer has the stress on the first syllable
• snart has a long vowel sound

The exact pronunciation depends somewhat on dialect, but that stress pattern is a good starting point.