NEET counselling for Tamil Nadu will be likely begin in the last week of June. So you can get the link to it then. When you register for counselling, they will produce a merit list of all the students that applied for counselling. 

If you want to apply for 85% seats in TN, then it is only for the residents. If you are not a residet of TN, then you can apply for 15% seats in All India counselling.

Hi, you can refer to the link below to view list of medical and dental, Government or private colleges in Tamil Nadu

https://medicine.careers360.com/articles/neet-cutoff-tamil-nadu

You can enroll for admission either through All India Quota(15% reservation) or State Quota(85% reservation) under the category yiu belong to i.e general/unreserved; OBC; SC; ST 

If you wish know about cutoffs if any other state, you can refer to the article in the link given: https://medicine.careers360.com/articles/neet-cut-off

I would suggest you to use the NEET college predictor to view the possibities of colleges in which you can get admission, because the cutoffs change every year depending on various factors like no.of seats available, no.of applicants, difficulty of paper and NEET results.The link of NEET college predictor https://medicine.careers360.com/neet-college-predictor 

To know how the predictor works, what are it's advantages etc refer to the article in the link  https://medicine.careers360.com/articles/neet-pg-college-predictor 

Good Luck