I'll have a go at the first two:
1. When you exercise the prop the rpm is reduced. The MAP reading is always below ambient (non-turbo) and this is caused by the 'suck' from the cylinders and the restricted orifice at the throttle. When you reduce rpm you are reducing the sucking from the cylinders and so the MAP has the chance to recover to nearer ambient - remember MAP is ambient pressure when the engine is shut down.
2. The sideslip will have little effect on the pitot head (unless you're talking horrendous sideslip angles) but will significantly affect the static vent. If you sideslip left with the static vent on the left side you will be adding some dynamic pressure to the static pressure its reading so you should expect a decrease in altitude, a momentary rate of descent until the sideslip stabilises and a decrease in IAS as the same total pressure is being reduced by an apparently larger static pressure. However, just to muddy the water, if the static vent is high on the side of a curved fuselage it is possible that it will get a lower static pressure in a sideslip as the fuselage is working like an aerofoil and dropping the static pressure.
3. Pass - Ask me one on sport.