MD

The Doctor of Medicine (MD) course is accredited by the Liaison Committee on Medical Education. To apply to Yale School of Medicine (MD) course, submit the AMCAS application. To complete the application process, the applicants of the MD course should submit an online Yale Secondary application, in addition to the AMCAS application. Letters of recommendation have to be submitted too. Also, submit the academic transcripts and other documents (as required).

The course duration for MD at PK DAS Institute of Medical Sciences - Hospital and Medical College is three years. Candidates must make sure to participate in the admission process to secure a seat. 
Candidates who get the final admission offer, must pay the course fee to start with the regular classes on campus. 

The specialisation specific seat intake for the MD and MS programmes at the PK DAS Institute of Medical Sciences - Hospital and Medical College is given in the table below: 

Ophthalmology is typically offered as MS (Master of Surgery) in India, although some institutions would offer it as an MD based on the academic structure of the institution.
Both paths will give you the same core competencies in training, however MS will generally have more of a surgical training emphasis.

Yes, there are many government MD colleges in Karnataka. Some of them are mentioned below along with their tuition fees:

As per NIRF ranking 2024, NIMHANS emerged to be as the top MD college in Karnataka. Listed below are the colleges along with their NIRF ranking over the past three years:

Disclaimer: This information is sourced from official website of the ranking body listed and may vary.

Urology is a super-specialty surgical field, so it comes under M.Ch. (Master of Chirurgiae) qualification. You pursue this qualification after doing an MS in General Surgery.
Neither MD or MS gives you a qualification of Urologist. MD is for medicine (non-surgical) while MS is a pathway to surgical specialties, including M.ch Urology.