Learn Portuguese (Portugal): Não podes vir? Que pena!

In Portuguese, you don't always need to include the subject pronoun (like tu for "you"). Because the verb poder (to be able to / can) is conjugated as podes, it is already clear that we are talking to "you" (informal singular). So, saying Não podes vir? is perfectly natural.

Why is vir left in its infinitive form instead of being conjugated?

Just like in English, when you use a verb like poder (can) followed by another verb, only the first verb is conjugated. The second verb, vir (to come), stays in its dictionary form (the infinitive).

Doesn't pena mean "feather"? How does Que pena! mean "What a pity!"?

It is true that pena means "feather", but it has a second meaning: sorrow, grief, or pity. The phrase Que pena! is a very common, everyday expression used to say "What a pity!" or "What a shame!". Notice that unlike English, Portuguese does not use an article here—it is just Que pena!, never Que uma pena!.

Why is the word order in the question Não podes vir? the exact same as a statement?

In Portuguese, you do not need to flip the word order or add extra words to ask a yes/no question. You just use the normal statement word order—Não podes vir (You cannot come)—and raise the pitch of your voice at the end to turn it into a question.