Manifold pressure is the pressure inside your intake manifold, pure and simple. Nothing more, nothing less.
Your manifold operates like a vacum cleaner hose. Your engine is the vacum cleaner. Close the throttle, and it's like putting your hand over the vacum cleaner hose opening. Pressure drops; the suction created by the engine continues, and there's no air passing the throttle butterfly to feed it. Pressure drops.
Open the throttle all the way on a normally aspirated engine, and the best you'll get is ambient air pressure. At sea level on a standard day, you'll get 29.92". It drops approximately an inch per thousand feet, so at five thousand feet, expect about 24 inches, max. (This is the primary reason that engines won't produce more than 75% power above approximately 3,000' density altitude, and consequently manufacturers recommend against leaning below that altitude, and recommend leaning above it).
The velocity of air through the carburetor or intake doesn't affect manifold pressure, except for a slight increase at higher airspeeds and propeller RPM's due to ram air rise.
As for Vmc and icing, it all depends on the icing. If you're talking engine icing, then this affects power output, and consequently Vmc. If you're talking airframe icing, it depends on the specific circumstances. Vmc is largely predicated on the moment arm of the rudder, against the moment arm of the critical engine. Any change in the moment of the thrust produced on an engine, or the CG arm for the rudder, will result in a change in Vmc.
Increase the CG arm, and Vmc goes down. Increase power on the critical engine, and Vmc goes up.
However, Vmc is the airspeed at which directional control can no longer be maintained with the critical engine windmilling, the good engine at takeoff power, gross weight, aft CG, banked 5 degrees into the good engine, and decreasing airspeed at the rate of one knot per second until directional control is lost. Any change from this produces a speed at which directional control may be lost, but it not actually Vmc. Therefore, ice may increase or decrease the speed at which directional control may no longer be maintained, but may or may not affect Vmc.
Generally speaking, ice will affect stall speed more than Vmc. Vmc by the definition in FAR 1.1 only stipulates that it is the minimum control speed with the critical engine inoperative. Under that more general definition, the Vmc speed will vary with ice, but stall speed will vary more. Other factors that can come into play are the uneven buildup of ice, tailplane icing and stalls, etc. These all affect controllability.
Ice decreases rudder effectiveness, and also decreases propeller efficiency. The rate at which these primary affecting factors occur can play a big part in weather or not Vmc appreciably changes with ice acceration.