do we have to register again for the second round of neet state (Maharashtra) counselling though we have registered for the first round? if yes, than when ?

No, you don't need to register again if you have done your registration in Round 1 of Maharashtra Neet State Counselling 2020. If you want to go for upgradation then you need to login to your account of Maharashtra State counselling and select the option. If you have allotted a seat and satisfied with it but also want to participate in the next round then you have to choose option 2. And if you are not satisfied with your seat so want to participate in next round for upgradation then you have to choose option 3 and act accordingly. Check out this link for detailed information about Neet Maharashtra State counselling and which option to choose http://medicine.careers360.com/articles/maharashtra-mbbs-counselling

No. If you have already registered for Round 1 of State Counselling, you needn't re-register. One registration is good enough for the entire counselling process. The counselling of Maharashtra NEET will be conducted by the Commissioner of State Entrance Exams. Maharashtra State counselling is conducted in two rounds. Seats left vacant or unfilled after the completion of the second round are filled in the mop-up round of Maharashtra NEET counselling. You can check them at our page: https://medicine.careers360.com/articles/maharashtra-mbbs-counselling .Please check the information brochure at: https://view.mahacet.org/mahacet/admin/news_document/FinalNEETUG%202020%20Informationrochure04112020.pdf