Hi 

The major thing which takes part in any counselling is that from where did you appear for the exam. For example if you appear from Karnataka you would be egligble for all indian colleges as well as get preference for your state colleges too. 

Not in the case that being a resident would help you to sit for Tamil Nadu counselling, if you're a resident of TN and want a college in same state you can appear for the state medical entrance test,

hope this answers your query,

cheers!