Learn Spanish (Spain): Quiero unas gambas con ajo. - I want some prawns with garlic.

Yes, you can say Quiero gambas to mean "I want prawns" in general. Using unas means "some prawns" or a specific portion. It is very natural when ordering a plate of food to share.

I have heard the word camarones before. What is the difference between that and gambas?

In Spain, gambas is the standard word for prawns or shrimp. Camarones is the word used in most of Latin America. Since you are focusing on Spanish from Spain, gambas is the word you will see on tapas menus!

Why is it just con ajo and not con el ajo?

When talking about a flavor or an ingredient mixed into a dish, Spanish leaves out the article (the word for "the"). You just use con plus the ingredient, exactly like saying "with garlic" in English.

Is it rude to order food by saying Quiero (I want)?

Not in Spain! While saying "I want" sounds demanding in English, Quiero is a completely normal and acceptable way to order food in a Spanish restaurant or bar. You can always add por favor to be extra polite!