Angenommen, dass die Veranstaltungstechnik fehlt, ändern wir die Bestuhlung.

Here, Angenommen means assuming, supposing, or let’s assume.

It comes from the verb annehmen and is originally a past participle, but in sentences like this it works as a clause opener for a hypothetical situation:

Angenommen, dass ... = Assuming that ...

So it is not being used with its everyday verb meaning to accept here.

Yes, it is grammatical, but it sounds a bit formal or written.

Many speakers would more naturally say:

• Angenommen, die Veranstaltungstechnik fehlt, ändern wir die Bestuhlung.
• Wenn die Veranstaltungstechnik fehlt, ändern wir die Bestuhlung.
• Falls die Veranstaltungstechnik fehlt, ändern wir die Bestuhlung.

The difference is mainly tone:

• angenommen = more hypothetical, like let’s assume
• wenn/falls = more ordinary if

So your sentence is possible, but not the most everyday way to say it.

Because dass introduces a subordinate clause, and in German subordinate clauses the finite verb usually goes to the end.

So:

• dass die Veranstaltungstechnik fehlt

not

• dass die Veranstaltungstechnik fehlt → correct
• dass die Veranstaltungstechnik fehlt with the verb somewhere earlier → not standard

This is one of the most important German word-order rules:

• main clause: verb in second position
• subordinate clause: verb at the end

Because the sentence begins with an introductory clause, and German main clauses still keep the finite verb in second position.

The whole opening part:

Angenommen, dass die Veranstaltungstechnik fehlt

counts as position 1.

So the main clause must begin:

ändern wir ...

Structure:

1. introductory clause
2. finite verb
3. subject
4. rest

So:

• Angenommen, dass die Veranstaltungstechnik fehlt, ändern wir die Bestuhlung.

This is normal German word order.

No, they are not in the same case, but they are both feminine singular, and for feminine singular the article die is the same in both nominative and accusative.

• die Veranstaltungstechnik = nominative, the subject of fehlt
• die Bestuhlung = accusative, the direct object of ändern

So the cases are different, but the article happens to look the same.

Fehlen means to be missing, to be absent, or to be lacking.

That is important because German often structures this idea differently from English.

In your sentence:

• die Veranstaltungstechnik fehlt
  = the event equipment is missing

If you want to say we are missing the event equipment, German often says:

• Uns fehlt die Veranstaltungstechnik.

Literally: To us, the event equipment is missing.

Also, do not confuse fehlen with vermissen:

• Ich vermisse dich. = I miss you.
• Der Beamer fehlt. = The projector is missing.

Veranstaltungstechnik is a compound noun:

• Veranstaltung = event
• Technik = technology / technical equipment / technical setup

In context, Veranstaltungstechnik usually means something like:

• event equipment
• technical event setup
• AV / sound / lighting equipment

It usually does not mean abstract technology in a broad modern sense. It is more about the practical technical setup for an event.

Because German very often combines nouns into a single compound word.

So instead of writing something like event technology as two words, German writes:

Veranstaltungstechnik

This is completely normal in German. A useful rule is:

• the last part usually determines the grammatical gender and the basic category of the word

Here the last part is Technik, which is feminine, so the whole compound is:

die Veranstaltungstechnik

Not exactly. Bestuhlung usually means the seating arrangement or chair layout in a room.

So:

• Stühle = chairs
• Bestuhlung = how the chairs/seats are arranged

Therefore:

die Bestuhlung ändern
means something like:

• change the seating arrangement
• rearrange the seating
• alter the chair layout

It is a fairly specific event/venue word.

There are commas because the sentence begins with an inserted introductory clause.

You have:

Angenommen, dass die Veranstaltungstechnik fehlt,
then the main clause: ändern wir die Bestuhlung.

So the commas mark the boundaries of that opening clause.

In German, commas are used very regularly with subordinate clauses, much more strictly than in English.

German often uses the present tense to talk about the future when the meaning is clear from context.

So:

ändern wir die Bestuhlung

can mean:

• we change the seating arrangement
• we will change the seating arrangement

In this sentence, the conditional setup makes the future meaning easy to understand.

If you wanted to make the future more explicit, you could say:

... werden wir die Bestuhlung ändern.

But the present tense is very natural in German here.