Using hot glue is advised if the computer is going to experience a lot of vibration. In an ordinary home desktop environment, it's unlikely that you'll need to use glue. I have a feeling that the designers were primarily concerned with protecting the components during shipping.

As to C1: Its failure results in a lack of horizontal deflection (so that you only see a vertical line down the middle of the screen), or weak deflection. These abnormal conditions can also have the secondary effect of causing the high-voltage circuitry to misbehave. Symptoms can range from a dim display to a completely dark one. And, on occasion, banshee-like screeching noises from the HV (flyback) transformer, followed by emission of the all-important magic smoke.