When flying a Jet Aircraft, What happens to Profile and Induced Drag with SPEED?

In principal aerodynamics are independent of the mode of propulsion. What I believe you're asking is what happens when you get up to near the speed of sound.

The short answer is: a lot changes when you are approaching M=1. Profile drag increases sharply and decreases again once you go faster than the speed of sound. However, the overall ratio of lift/drag will be worse at supersonic speeds. At transsonic speeds (M is close to 1) another form of drag starts to become important: interference drag. It is due to shock waves from different parts of the aircraft structure interfering with each other thereby increasing overall drag.

The aircraft design in its entirety will be different if you intend to go at speeds M>1. In general, it will turn out ot be a compromise between absolute speed and efficiency. Therefore, supersonic aircraft will be able to go significantly faster but at the expense of fuel economy.

-- Chris.