can i attend AIQ counselling and state counselling together

Yes, you can appear for both All India counselling and state counselling. All India counselling is conducted by DGHS while State counselling is conducted by respective state counselling authorities. The applications for both the counselling are different. October 28 onwards the registration for All India counselling has been started. On the other hand, many states like Goa, Puducherry has started the state counselling process while many states are yet to inform their counselling schedule. Check out this link for Neet counselling http://medicine.careers360.com/articles/neet-counselling