Throws are common in many martial arts, not just Aikido or Judo.
Injuries will depend entirely upon the training of the school. The two things will be if they train the students to fall correctly and if they actually do full power throws. Also the equipment the school has will help. Are there mats to practice on? Does the instructor gradually bring the students along or will he throw them hard to show he's the man?
MArtial arts deal with the knowledge and application of violence. Even with the best of circumstances and teachers you run the risk of being injured. Its part of what we do.