Learn Portuguese (Portugal): Quero carne grelhada com salada.

In Portuguese, the verb ending usually tells you who is doing the action. Quero is the "I" form of querer (to want), so adding Eu is optional and typically left out unless you want to emphasize it.

Why is it carne grelhada instead of grelhada carne?

In Portuguese, descriptive words (adjectives) almost always come after the noun they describe. Also, because carne is a feminine noun, the adjective must match it, changing from grelhado to grelhada.

Why isn't there a word for "the" or "some" before carne or salada?

Just like in English, when you are talking about an unspecified amount of something general like meat or salad, you do not need to use an article. You can just say carne instead of a carne or uma carne.

Does carne mean beef specifically, or just any meat?

Carne translates simply to meat in general. If you wanted to specify beef, you would say carne de vaca. For pork, it would be carne de porco.