For criticism 2,  it is to be emphasized that whether you can "observe" simultaneous action doesnot matter. Cournot's conjecture is that, given a guess on its rival's action, a firm makes its own action, and then given this, its rival then makes the next action, so on and so forth. This process  is by assumption so quickly that  an  equilibrium is observed  immediately. But just keep in mind that Cournot's focus is on this soon "mental practice", not observable real actions.

Welcom discussion on criticisms 1and 3. Thx.

In the first criticism, when you say "Cournot", you can no longer say "normally", because cournot oligopoly normally does not exist. "Firms" who choose to set prices are normally from other market structure, not the cournot structure. Under a perfect cournot structure, only two firms exist, they are likely to set quantities. The generalization from other market structures does not apply in  cournot structure.