Of course. Australian Galahs speak like Australian people. The birds aren't actually learning words, they're mimicking sounds. An accent is the sound of a pronunciation. If a parrot is only mimicking sounds with no understanding, it would of course, mimic the accent.
Only to an outsider. Fun fact! Crows have developed a language, it is so ordered that there are actual dialects depending on the crow's location. ie a crow from California sounds different than one from Newfoundland. http://www.cracked.com/article_19042_6-terrifying-ways-crows-are-way-smarter-than-you-think.html
If they are learning the language of the land, I guess they say the words with the natural accent being spoken by the people teaching them.
Not to their original owner
You only have "accents" when you speak in a language other than your native tongue. So the answer is no.
Things that make you say Hmmmm??? lol
why don't you ask one?