In Spanish, esta noche is the normal way to say tonight.
So literally it is this night, but idiomatically it means tonight.
Hoy noche is not the usual expression in standard Spanish. A learner should strongly prefer esta noche.
Spanish often drops subject pronouns when they are clear from the verb ending.
Here, quiero already tells you the subject is I:
So Esta noche quiero pedir una pizza para cenar is completely natural.
You can say Yo quiero..., but it usually adds emphasis, contrast, or clarity:
Without that special reason, leaving out yo sounds more natural.
Here pedir means to order.
More literally, pedir often means to ask for or to request, but in food contexts it is the standard verb for ordering:
This is the most natural verb in Spain for ordering food from a restaurant or takeaway.
Usually, in Spain, pedir is the better and more natural choice for food.
In many contexts, ordenar more often means:
So if you are talking about ordering food, pedir is the safer and more idiomatic option in Spain.
Spanish usually needs an article here.
In English, we sometimes omit the article in certain food expressions, but in Spanish you would normally say:
Leaving out una would sound incomplete in most normal situations.
Para cenar means for dinner in the sense of to have for dinner / in order to eat at dinner time.
It uses para + infinitive to express purpose:
This is very natural in Spanish.
Para la cena is also possible, but it feels a bit more like for the dinner meal or for dinner as a noun phrase. In everyday speech, para cenar is often the more natural way to express the idea in this sentence.
Yes, Spanish word order is often more flexible than English.
The original sentence:
You could also say:
Both are correct. Starting with Esta noche simply puts the time expression first, which is very natural and often sounds like Tonight, I want to order a pizza for dinner.
So the original word order is normal, but it is not the only possible one.
It is completely natural in Spain.
Esta noche quiero pedir una pizza para cenar sounds like normal everyday Spanish. It is exactly the kind of sentence a native speaker might say when deciding what to eat.
The most Spain-friendly part is especially pedir una pizza, since pedir is the standard everyday verb for ordering food.