Learn Spanish (Latin America): La emergencia sanitaria empezó a causa de un restaurante sucio. - The health emergency started because of a dirty restaurant.

The connector a causa de translates to 'because of' or 'due to' and is followed by a noun or noun phrase, like un restaurante sucio. If you wanted to use porque (because), you would need to follow it with a full clause containing a conjugated verb, such as porque un restaurante estaba sucio (because a restaurant was dirty).

Do I need to add que and say a causa de que in this sentence?

Not in this sentence. You only use a causa de que when the cause includes a conjugated verb (a full clause). Because un restaurante sucio is just a noun phrase without a verb, you drop the que and just use a causa de.

Could I use por culpa de or gracias a instead of a causa de here?

You could definitely use por culpa de (through the fault of), since a dirty restaurant causing an emergency is a negative thing and someone is to blame. However, you cannot use gracias a (thanks to). Gracias a is strictly used for positive outcomes. A causa de works perfectly here as a slightly more formal, objective way to state the cause.

Why is 'health emergency' translated as emergencia sanitaria instead of emergencia de salud?