Familien er rik.

Because -en is the definite singular ending for this noun.

• en familie = a family
• familien = the family

So Familien er rik literally means The family is rich.

The dictionary form is en familie.

That tells you:

• the noun is usually treated as a common-gender noun
• the indefinite singular is en familie
• the definite singular is familien

Other useful forms are:

• familier = families
• familiene = the families

Er is the present tense of the verb å være (to be).

So:

• jeg er = I am
• du er = you are
• han/hun er = he/she is
• familien er = the family is

Norwegian does not change the present-tense form the way English does. It is just er for all persons.

Because rik agrees with a singular common-gender noun here.

Familie is a common-gender noun, so in this sentence:

• Familien er rik = The family is rich

Compare:

• et land er rikt = a country is rich / the country is rich
  
  • rikt is used with a singular neuter noun
• familiene er rike = the families are rich
  
  • rike is used in the plural

So the form rik is the correct one for familien.

Yes. Rik is an adjective meaning rich.

In this sentence it comes after er, so it is being used predicatively:

• Familien er rik = The family is rich

Compare that with an attributive use, where the adjective comes before the noun:

• en rik familie = a rich family

Because Norwegian often puts definiteness at the end of the noun instead of using a separate word like English the.

So:

• English: the family
• Norwegian: familien

That -en ending already contains the idea of the.

It is treated as singular here.

So Norwegian says:

• Familien er rik
  literally: The family is rich

Even if a family contains several people, the noun familien is grammatically singular. That is why the verb is er and the adjective is singular rik.

Yes, but Familien er rik is the normal neutral order.

This is the basic pattern:

• Subject + verb + adjective
• Familien + er + rik

You may sometimes see a different order for emphasis or in a larger sentence, but for a simple statement, Familien er rik is the most natural form.

A simple approximate pronunciation for an English speaker is:

• familien ≈ fa-MEE-lee-en
• er ≈ air / a short Norwegian e-r sound
• rik ≈ reek

A rough full approximation:

• fa-MEE-lee-en air reek

A few notes:

• The r is usually clearly pronounced.
• The i in rik is a long ee sound.
• The rhythm is fairly even compared with English.

In this sentence, yes, the most natural meaning is wealthy.

But rik can also be used in broader senses, depending on context, such as:

• rik på erfaring = rich in experience
• et rikt språk = a rich language

Still, if you see Familien er rik by itself, most people will understand it as The family is wealthy.

Yes, but it means something different.

• Familien er rik = The family is rich
  
  • a specific family
• En familie er rik = A family is rich
  
  • one unspecified family

So the original sentence is talking about a particular family, not just any family.