That's a statement, with a question mark and shifted spoken emphasis to make it into a question.
Swedish can do the same trick, but it did not do so here so you shouldn't do it in the translation.
The equivalent word-order for that would instead be: Han sjunger på tisdagar?
That's because putting the verb in the second position makes it a statement which gets forced into a question by the punctuation.
That's right. In statements verb always comes second. When it's a first word, that means it's a question.