The verb can indeed be used in a similar way to habiter, but it is generally of a more formal register, not so much like English "dwell", but more like reside (cf. He resides in Canada.).
The verb is also sometimes used instead of rester, to mean remain.
See the examples under demeurer in the section on avoir and être.
we use AU because Canada is a male word in french, and we use EN when the country is a female word.
so we say for example:
j'habite en France (la france)
j'habite en Italie (une italie)
j'habite en Russie (la russie)
et
j'habite au Portugal (le Portugal)
j'habite au Japon (le japon)
....
When the country has a plural name, then aux is generally used:
J'habite aux États-Unis.
Other examples would include Pays-Bas, Seychelles...
Incidentally, just to add to the complication, there are a few (generally feminine) countries which are islands, which many speakers use without the article at all. For example:
J'habite à Cuba. J'habite à Malte. J'habite à Taïwan.
You can just ask "Où habites-tu ?" (formal) or "Tu habites où ?" (grammatically incorrect, but conversational).
"Where are you from" would be "D'où es-tu ?" (formal) or "Tu es d'où ?" (incorrect but conversational).
Of course you can refine the question, for instance with "de quelle ville" (from which city) or "de quel pays" (from which country) instead of "d'où" (where from).
By the way, you can see that in conversational French, it's very, very, very common to place question words like "quand", "où", "d'où", "comment", "qui" at the end of the sentence, not at the beginning. And when it happens, the subject and the verb aren't swapped.
Formal:
Où habites-tu ?
D'où viens-tu ?
Quand allez-vous au cinéma ?
Qui as-tu vu ?
Comment t'appelles-tu ?
Incorrect, but very, very, very common in real speech (and sounds like a native speaker):
Tu habites où ?
Tu viens d'où ?
Vous allez au cinéma quand ? ou : Vous allez quand au cinéma ?
Tu as vu qui ?
Tu t'appelles comment ?
The "Que" word can also be placed at the end of the sentence, but it becomes "Quoi" :
Que fais-tu ? => Tu fais quoi ?
Que lis-tu ? => Tu lis quoi ?
Que manges-tu ? => Tu manges quoi ?
You can use this structure in emails to friends, but never use it in formal letters. But try to use it in speech. Even with your boss, you can use it.
"Tu" vs "Vous" is confusing to English speakers, because both mean "You".
"Tu": applies to only one person. You should use "tu" with anyone you know very well, like friends, relatives, colleagues, etc. You shouldn't use "tu" with someone you meet for the first time or someone you need to show respect for.
"Vous": applies either to a group of persons, or to an individual that you need to show respect for, or that you don't know much.
So:
- "Où habites-tu ?" or "tu habites où ?" : this is what you would say to a friend
- "Où habitez-vous ?" or "vous habitez où ?" : this is what you would say to a group of friends. Or this is what you would say to a stranger. Or this is what you would say to your boss (unless he looks cool enough to be considered as a friend).
If you hook up with a French girl, start with "Vous" and don't switch to "Tu" before she has disclosed her first name :)
Incidentally, beware of using words like "correct" and "incorrect" (in French or English!)-- it can be a bit ambiguous what you mean. Sometimes people use "incorrect" to mean "ungrammatical" (i.e. a native speaker would generally not judge the sentence to be a possible, well-formed sentence of French). And sometimes people use it to mean "not conforming to some prescriptive etiquette".
A form such as "Tu fais quoi là?" belongs to normal, everyday speech. But so what? Why should normal, everyday speech be the stigmatised form? If what you're trying to describe is everyday French, then an utterance such as this is a perfectly grammatical utterance of French. From that point of view it's "correct". Similarly, you might label the questions "Pourquoi que les fous c'est nous?", "Quelle heure qu'il est?" as being 'slang', 'popular', 'non-standard' etc. But if you imagine a certain number of native French speakers using them, there's a point of view according to which they're still "correct".
But on the other hand, it is of course worth pointing out when forms are considered everyday, informal, formal, literary, slang, stigmatised etc. But I think these more detailed labels are more useful than "incorrect" vs "correct".