Science

B.Sc. Nursing in Pink City College of Nursing is a 2 year degree course.
The annual fees for it is Rs. 70,000.

To pursue B.Sc. (H) Agriculture in Oriental University you can directly apply through the college portal OR visit the university for offline application. No entrance exam is as such needed.
Eligibility - 12th passed( AG/ PCM/PCB) with min 50% (Gen) and 45%/ 40% (OBC/SC/ST)

Cut-offs keep changing depending on the no. of applicants, complexity of exams etc. For B.Sc Nursing cut-off for female candidates is usually less by 3-4 than male candidates.
Below is the rough estimate for getting admission in S.M.S. Medical college .
Gen 85
OBC 82
EWS 82
MBC 80
SC 78
ST 77

The candidate applying for B.Sc. Nursing must have an eligibility of 10+2 and at least 50% marks in aggregate with Biology Chemistry and Physics as compulsory subjects. It is an undergraduate level programme which conducts an entrance exam in the month of April every year. Its age limit is not less than 17 years of age as per the current year. It is an 4 year paramedical course. The entrance test is conducted by University of Jammu and Kashmir.

Toatal 3 year fees for B.Sc (Maths/Bio) is around six thousand rupees.

Yes, there are vacancies available.

Pediatric Surgeon. Upper Gastro-Intestinal Surgeon. Urological Surgeon. Vascular Surgeon. Resident (General Surgery) Cardiothoracic Surgeon. Endocrine Surgeon.

Yes, you are eligible.

I believe you are referring to your ICAR AIEEA rank of 50585, as the total score for this exam is 600. Well, your rank is too high to get admission to any government agricultural university. There may be some chance that you get admission to your state agricultural, veterinary, horticultural, or fisheries university (SAU). For admission to your state university, either your category rank must be good or your score must be higher than 280. You can get the idea of the previous year's cut-off rank and scores for SAUs by visiting this Shiksha page: https://www.shiksha.com/science/icar-aieea-exam-cutoff.

The answer is it depends on the college from which you are pursuing your degree it can range from 2L per annum to 5 L per annum which varies from college to college.