Answer to "My tether for my controller is worn."Yes you just need to contact Leap Frogs customer support and they can send you a new one. For safety reasons stop using the controller until you have replaced the broken tether.
Answer to "Can I use a computer monitor?"You can use a computer monitor as long as there is an HDMI port and built-in speakers.
Answer to "What is the battery life?"You should expect 24 hours of play time out of two AA alkaline batteries. This can vary depending on which mode you have the controller in.