I was just thinking, in the event if both players have an Lv 0 Alice in their friend area, do you have to discard 2 friend cards instead of one, for each Lv 0 Alice, during the Discard phase?

Yes, the effect stacks.

The effect works like Jack (in terms of stacking) and Luna is right. Almost, can not vouche for all, all effects like Jack, Alice, Black Fungus, etc. stack.

Yes the effect stacks, also you cannot discard a magic/friend or the King to satisfy the effect of Alice