For the most part, yes. Whenever you get a blue screen on your monitor, no matter the shade, it is bad news. I recommend taking to a professional to see if it is even worth saving. It can be expensive.
This blue screen is what i like to call the blue screen of death. This means that your computer has seen better days and most likely means its time to get a new computer. If you dont have to moeny for one, take it in to a professional company and you can get it fixed for a fair price.
No, it does not mean that the Computer Monitor has gone bad. In most of the cases, it is due to bad connection with the Video Card. It can be a loose connection or it can be that the cable is faulty or broken.
Not necessarily. You should try the monitor on another computer if possible and update any the video and motherboard drivers for the system it isn't working with.