Alexander was raised by her mother in Mannheim. Alexander is of Arab descent - her father was born and raised in Ramallah.
As a teenager she was a sensei and some of her students were football hooligans. She would attend football matches with them but drifted away after she felt they overstepped their bounds. In 1993, at the age of 19, Alexander became world champion in both point fighting and karate. She then retired from professional fighting and moved to the US, where she landed the part of Kitana in Mortal Kombat: Live Tour.
In June 2014, Alexander criticising the anti-piracy actions of Hollywood on her official website, as well as its general "lack of diversity" and gender and racial inequalities that she notes exist in Hollywood, referencing articles from both the UCLA and other news/opinion sites. Alexander, however, made it clear that she does not endorse piracy. In fact, she noted that key individuals in the piracy scene, such as Kim Dotcom are "not Robin Hoods", saying in the case of Dotcom: "he's got a big house, a lot of luxury cars and all kinds of other toys [...] This is unfortunate, because in a way it makes him just like the Hollywood elite". She also mentioned about The Pirate Bay's association with Carl Lundström - a Swedish businessman who financed the right-wing Swedish Progress Party, which later merged with the Sweden Democrats (The Pirate Bay accepted funding for their servers from Lundström). Despite a clear criticism of both Hollywood and its anti-piracy agenda and key figures in the pro-piracy scene, as well as clarifying that she does not endorse piracy, she stated "[t]here's a real opportunity for someone to come in and turn our industry into something better". She finalised her post with a daring picture of her holding up a sign reading, "Free Peter Sunde Now", in reference to his prison sentence as part of The Pirate Bay trial.