Re: Khula or divorce
Someone I know got her Nikah done with a guy in Pakistan - Islamically and legally. They were going to do the rukhsati once he got his papers for Canada. Unfortunately things didn't work out between the two and she asked for a divorce. He refused to divorce her point blank. He said the only way he was going to divorce her was if she brought him over to Canada first. Once he got here, he'd be more than willing to divorce her. She was quite angry so she went to the court to get a legal divorce.
Is the legal divorce also an Islamic divorce - well, there is a difference of opinion in that matter. There are two schools of thought on this issue. The majority says if the legal system of the country in which you reside nulls the marriage, then that is also an Islamic divorce. More conservative scholars would say otherwise.
To answer your other question: getting married Islamically and legally is most countries are two different things. Just because you have your nikah done, doesn't make you a married couple according to the courts. A marriage must be registered to be considered legal - in Canada, anyway. Otherwise, you're considered common-law according to the stats.