Same answer to all three questions. It is the center of mass that newton's First and Second laws apply to.
In question One there is no external force or moment, so the linear and angular momentums remain constant. In question 2 the center of mass of the projectile continues along the same parabolic path that it did when it was all one body. The same applies to the star in question 3. The center of mass does not wobble, therefore the star is not alone but there must be at least one other body like a planet other other star that is interacting with the star and the center of mass of the star-planet system does not change its momentum.
1) What part of an object follows a smooth path when the object is made to spin through the air or across a flat smooth surface?
2) Describe the motion of the CG of a projectile, before and after it explodes in midair.
3) What is suggested by a star that wobbles off center?
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