Government Medical College, Nagpur

Yes, you can apply with your NEET score card. Other state students can apply also. All the best.

Yes, if you have good marks and meet the eligibility requirement, then one can take admission.

Hello Sulochana,
The minimum marks required are kept at 45% as per Maharashtra Nursing Council for Admission into B.Sc. Nursing. I am attaching a link that will give you all the required information:
http://www.maharashtranursingcouncil.org/Eligibility.aspx

Reputed institutes follow merit based admission process. Under this scheme, marks scored by students in 10+2 board examination and/or relevant entrance test (national, state or institute-wise) are taken into consideration. Seats are allotted to deserving candidates on the basis of merit marks obtained by them.

Under 15% All INDIA Quota, the last cut-off rank in which students got admission was approx. 8300, that too in the 2nd round of counselling.
For every state, the cut-off will vary.

There are the chances that you have been selected for B.Sc Nursing. If don't, then also don't bother so much because you have so many opportunities around you regarding where to do B.Sc nursing. The ultimate goal would be, do best among all and learn all the skills related to that field so that nobody can beat you. For e.g., there is one friend of mine who has 60% in 10+2 and one of my friend has 89. Both have appeared to CBSE-PMT. One who has 60% got admission and 89% hasn't, it was a general example. So keep motivating yourself and keep targeting your goal.

Just as simple as that is you need a good score in turn a better rank. Participate in both state and AI counselling and choose the seat you like.