In the pronominal sense of "the entire/whole" or "all of", only hela is used, without an article, and followed by a definite form. Same with other similar words, such as halva 'half of' or båda 'both of'. (Note the sense of measuring/specifying with these words)
If you use it with an article you'll get the other sense of the word, 'whole' as in 'unbroken'.
Hela huset = The entire house
Det hela huset = The unbroken house
Exactly – just like in Swedish, it varies with the word. Blehg explains it pretty well in his comment above. There's a group of adjectives that behave this way. What they have in common is that they are all words that sort of make the word definite all by themselves. For instance if I say next week, we both know which week I'm talking about, so we don't need anything more to make it definite. So we just say nästa vecka. Adjectives in this group are adjectives that refer to order (like nästa, also sista 'last', förra 'last/previous', första 'first', andra second etc). They tend to be a little irregular in what they prefer though: we say nästa vecka 'next week' but förra veckan 'last week'.
Pronouns such as samma 'same' (samma bok 'the same book') and all possessive pronouns (min bok, 'my book') also have this 'definite enough' effect.
The voice is not quite perfect on this sentence, as of August 11th, 2017, so I've taken the liberty of re-recording it.
The stress should be on hela MÅnaden, rather than on HEla månaDEN like the voice does. Further, since it's a question, the pitch should change.
Please find a correct recording on http://duolingo.vydea.io/bdc033ccb543456b865914c21d199f29.mp3, which contains first a recording of the question version, followed by a recording of the statement version.
For more info on re-recordings, please check the info thread: https://www.duolingo.com/comment/23723515
Thanks for listening. Ha en bra dag! :)