Is the taxi in Livingstone safe? Can I get a taxi easily from airport?
Yes they are safe. Look for the cars with a purple stripe running around the side, those are the official taxis.
What do they cost
If you are interested in a safe way to travel, I may have an option for you. We utilized Kativu Tours & Travel when we were in Africa this past summer. They are a small tour company based out of Victoria Falls, consequently, they are cheaper and know the culture. I think you would be pleased.