One more thing if the date of registraion has been exceeded then also you cannot go for the registration. After the date you cannot apply. So kindly check for your state that the registrations are still going on or not.

You can participate in the first round and there is no criteria that the first round needs mock round to be attended. So if you have registered yourself and you have paid the application fee then you can go for the further rounds of counselling. Mock round is just for the idea of getting the college as per the merit marks and there is no such criteria for attending the rounds.