Learn Portuguese (Portugal): Nós grelhamos peixe na praia.

It means "we grill" (present tense). In European Portuguese, the past tense of -ar verbs adds an accent mark to the letter a, like grelhámos, which also changes the pronunciation to a more open sound. Because there is no accent here, we know it is happening in the present.

Do I always have to include the word Nós?

No, you can usually leave it out. The -mos ending on the verb grelhamos already makes it perfectly clear that the subject is "we". Including Nós just adds a little bit of emphasis.

Why isn't there an article like o before peixe?

Just like in English, you do not need to use an article when talking about an unspecified amount of food or a general category. Saying o peixe would mean "the fish" (a specific one you already mentioned), but here they are just talking about grilling fish in general.

Why is "at the beach" translated as na praia instead of à praia?

The word na is a contraction of the preposition em (in/at/on) and the feminine article a (the). You use em to talk about a stationary location where an action is happening. You would use the preposition a (which combines with the article to make à praia) if you were talking about movement towards a destination, like going to the beach.