I am fascinated by the concept of supercharging and turbocharging an engine to maximize air compression (and thus fuel use) in the charged engine. I understand the basic concept of superchargers using a pulley system to force more air into the engine via power from the engine crankshaft and of turbochargers using the engine exhaust stream to accomplish this. I also have heard of the three main types of supercharger (roots blowers, twin-screw and centrifugal SC's).

Questions:
1. Is one particular SC system (regardless of cost) "better" than another, or more safe?
2. Is it possible to simultaneously supercharge and turbocharge an engine (to obviate the turbocharger's lag at lower rpm's) or is this not safe due to overcompression of the air fuel mixture?
3. Could a combo. SC/TC engine be sufficiently cooled and of low additional weight to improve performance ?