Angular momentum is the rotational analogue of linear momentum with the formula:
It can also be further derived as:
$$ L=(mr^2)\left(\frac vr \right)=mvr$$
$r$ being the radius from the center of the mass to the rim, then we can logically deduce that angular momentum is directly proportional to angular velocity and angular velocity is inversely proportional to the radius. So if the angular momentum is conserved, an increase or decrease in radius translates to a decrease or increase in angular velocity respectively.
For the other questions, if by loosing the outer shell you mean the shell collapses into the rest of the mass to form a denser mass with less radius, the top speeds up. If the shell just vanishes off the mass and cease to exist (hypothetically), the top will start spinning a lot lot more, depending on how much mass and radius is lost. Also if the shell comes off the mass by breaking or ripping apart, the mass keeps spinning at the same rate.