Telefonen ringer derinde.

In Danish, the definite article is usually attached to the end of the noun.

• telefon = phone
• en telefon = a phone
• telefonen = the phone

So -en is doing the job that the does in English.
This happens because telefon is a common-gender noun. If it were neuter, the definite ending would usually be -et instead.

Ringer is the present tense of at ringe.

• at ringe = to ring / to call
• ringer = rings / is ringing / calls / is calling

In this sentence, because the subject is telefonen, the natural meaning is that the phone is making a ringing sound.

Because Danish usually does not form the ongoing present the way English does.

English often distinguishes:

• The phone rings
• The phone is ringing

Danish very often uses the simple present for both ideas:

• Telefonen ringer

So the sentence can mean either a general present or something happening right now, depending on context. With a phone, it will often be understood as happening now.

Derinde is an adverb meaning in there or inside there.

It combines the idea of:

• der = there
• inde = inside / indoors

So derinde points to a place that is inside and not here with the speaker. If the speaker meant in here, Danish would often use herinde instead.

That is normal Danish word order.

The sentence has the basic pattern:

subject + verb + adverbial

So:

• Telefonen = subject
• ringer = verb
• derinde = adverb of place

A neutral statement often puts the place expression after the verb like this.

Yes. That is also grammatical.

Danish main clauses normally follow the verb-second rule, which means the finite verb stays in the second position. So if you move derinde to the front, the verb must still come second:

• Telefonen ringer derinde
• Derinde ringer telefonen

The second version gives more emphasis to the location, something like In there, the phone is ringing.

Usually, yes. Derinde is commonly written as one word when it functions as this adverb.

You may sometimes see der inde as two words in other contexts or with a slightly different emphasis, but derinde is a good standard form for learners to use in a sentence like this.

Yes. At ringe can mean both:

• to ring
• to call / phone

The subject usually makes the meaning clear.

• Telefonen ringer = The phone is ringing
• Han ringer = He is calling / phoning

So in your sentence, because the phone is the subject, the meaning is the ringing sound.

You could, but they do not mean exactly the same thing.

• inde = inside / indoors
• der = there
• derinde = in there

So derinde is more specific because it combines both ideas.
Telefonen ringer der only says the ringing is there, not necessarily inside.
Telefonen ringer inde may work if the inside location is already obvious, but it is less precise than derinde.

Yes, it does. It is a normal, natural sentence.

It sounds like a straightforward observation: the phone is ringing somewhere inside, away from where the speaker is. There is nothing odd or overly formal about it.