De deur gaat niet open, dus ik vraag de conciërge om hulp.

Because opengaan is a separable verb.

In a main clause, the conjugated verb goes to the second position, and the separable part moves to the end:

• De deur gaat niet open.

If the verb is in an infinitive or in a subordinate clause, it stays together:

• De deur wil niet opengaan.
• Omdat de deur niet opengaat, vraag ik de conciërge om hulp.

So the sentence is showing the normal split form of opengaan.

Dutch usually uses opengaan for something that opens by itself or simply changes from closed to open:

• De deur gaat open. = The door opens / goes open.

Openen is more often transitive, meaning that someone opens something:

• Ik open de deur. = I open the door.

So De deur gaat niet open is the most natural everyday way to say that the door will not open.

Because in this kind of sentence, niet usually comes before the part it is negating, and with a separable verb that often means it appears before the final particle:

• De deur gaat niet open.

That is the normal word order.
De deur gaat open niet is not correct Dutch.

In this sentence, dus is linking two main clauses, and the second clause keeps normal main-clause order:

• De deur gaat niet open, dus ik vraag ...

So the subject ik comes before the verb vraag.

A useful comparison is daarom, which does trigger inversion when placed first:

• De deur gaat niet open, daarom vraag ik de conciërge om hulp.

So dus ik vraag is correct here.

Because the subject is ik, and in the present tense Dutch usually uses the bare stem with ik:

• ik vraag
• jij vraagt
• hij vraagt

So ik vraag is the correct form.

Because Dutch commonly uses the pattern:

• iemand om iets vragen

That means to ask someone for something.

So:

• ik vraag de conciërge om hulp

literally follows the Dutch structure ask someone for help.

You may also hear forms with aan, especially in speech, but iemand om iets vragen is the standard pattern learners should know first.

The preposition om belongs to the fixed expression om hulp vragen.

So Dutch says:

• om hulp vragen = to ask for help
• om advies vragen = to ask for advice
• om toestemming vragen = to ask for permission

You should learn vragen om as a set pattern when the meaning is ask for.

Because hulp here is being used as a general, uncountable noun: help in a general sense.

So Dutch normally says:

• om hulp vragen

not

• om de hulp vragen

Using de hulp would make it sound like a specific, already known help, which is not what this sentence means.

The trema on ë shows that this vowel is pronounced separately and starts a new syllable. It helps prevent you from reading the vowel combination as one single sound.

So conciërge is pronounced in separate parts, roughly like:

• kon-see-AIR-zhuh

The exact pronunciation can vary a bit, but the ë tells you the vowels are not merged.

Then the separable verb becomes one word again:

• Omdat de deur niet opengaat, vraag ik de conciërge om hulp.

That is a very important Dutch pattern:

• main clause: gaat ... open
• subordinate clause: opengaat

The same thing happens with many other separable verbs.

Yes. That is a very natural alternative.

• De deur gaat niet open, dus ik vraag de conciërge om hulp.
• De deur gaat niet open, daarom vraag ik de conciërge om hulp.

Both are good, but the word order changes with daarom:

• dus ik vraag
• daarom vraag ik

So the meanings are close, but the grammar is slightly different.