Is this right to inject the container/kernel to the main application presenter? [duplicate]

Answer 1

You should never pass the DI Container around, because then you're using it as a Service Locator, which is an anti-pattern.

If your ApplicationPresenter requires an AuthenticationPresenter and an InquiriesManagementPresenter, then inject those dependencies:

public class ApplicationPresenter : Presenter<IApplicationView>, IApplicationPresenter
{
    private readonly static AuthenticationPresenter authenticationPresenter;
    private readonly static InquiriesManagementPresenter inquiriesManagementPresenter;

    public ApplicationPresenter(
        IApplicationView view,
        AuthenticationPresenter authenticationPresenter,
        InquiriesManagementPresenter inquiriesManagementPresenter) 
        : base(view)
    {
        this.authenticationPresenter = authenticationPresenter;
        this.inquiriesManagementPresenter = inquiriesManagementPresenter;
        View.Connect += OnConnect;
        View.ManageInquiries += OnManageInquiries;
    }
}

If those presenters have dependencies of their own, it's totally fine: you just build up the entire graph up front, but the AplicationPresenter doesn't have to see any of the sub-graphs.