newtonian mechanics - Role of friction during pure rolling

I am confused about the role of friction during pure rolling. I tied to analyse these two cases:

Case 1: An object is rotated rapidly and put on a frictionless (smooth) table, will it execute pure rolling?

Case 2: The same object is rotated rapidly, kept on the smooth table and slightly pushed, will it now execute pure rolling?

For case 1, because there's no friction on the table, I feel that the object will keep sliding on the table but what about the rotation? Will that be hindered or not?

For second case, I feel that whatever be the magnitude of the push force, the same thing will happen i.e. the object will slide.

I am very unsure about my analysis. Also, there's this article in my book which has puzzled me more:

In accelerated pure rolling if $a = R\alpha$, then there's no need of friction and force of friction $f=0$.

Different people on different sites like Quora, give different contradicting answers.