Ørkenen er tørr.

In Norwegian, the definite article is usually added to the end of the noun.

• en ørken = a desert
• ørkenen = the desert

So the ending -en is doing the job that the does in English.

Er is the present tense of å være, which means to be.

So:

• er = is / am / are, depending on the subject

Norwegian does not change this form for different persons:

• jeg er = I am
• du er = you are
• ørkenen er = the desert is

Because tørr is the form used with a singular common-gender noun in this kind of sentence.

Here, ørkenen is singular and common gender, so the adjective stays:

• Ørkenen er tørr. = The desert is dry.

Compare:

• et område er tørt = an area is dry
  because område is neuter
• ørkener er tørre = deserts are dry
  because it is plural

Ørken is normally a masculine noun in Bokmål, often grouped under common gender in learner materials.

Its basic forms are:

• en ørken = a desert
• ørkenen = the desert

That is why you see -en in the definite singular.

The sound ø does not exist exactly in standard English, but you can get close.

A useful approximation:

• make a vowel similar to the one in British English bird
• but keep your lips more rounded

So:

• Ørkenen is roughly UR-ke-nen, but with rounded lips on the first vowel
• tørr is roughly like turr, again with rounded lips

Also, the double consonant in tørr helps show that the vowel is short.

Yes, you could.

• En ørken er tørr = A desert is dry
• Ørkenen er tørr = The desert is dry

Both can be used for general statements, but they feel slightly different.

• En ørken er tørr talks about a desert as a type
• Ørkenen er tørr can sound more like the desert as a landscape or concept, or a specific desert if the context is clear

Here are some useful forms.

For ørken:

• en ørken = a desert
• ørkenen = the desert
• ørkener = deserts
• ørkenene = the deserts

For tørr:

• tørr = common-gender singular
• tørt = neuter singular
• tørre = plural and many definite forms

Examples:

• en tørr ørken
• et tørt område
• tørre ørkener

Yes. When an adjective comes directly before a noun, it follows the normal adjective agreement pattern.

Examples:

• en tørr ørken = a dry desert
• et tørt område = a dry area
• tørre ørkener = dry deserts
• den tørre ørkenen = the dry desert

So in Ørkenen er tørr, the adjective comes after er, but before a noun it may need a different form.

No, this is the basic word order for a simple statement:

• subject + verb + adjective

So:

• Ørkenen = subject
• er = verb
• tørr = adjective

This is very normal Norwegian sentence structure.