KCET

10k ranking is too much for getting into CS department in BMSCE. Well, you can get into other branches in BMSCE itself (if you are interested any other branches).

The Medium of the question paper will be English. For more details, click below
https://www.shiksha.com/b-tech/kcet-exam-pattern.

You have not mentioned about the category you belongs. However, the opening and closing ranks in year-2018 for general category for BE-CSE from DSCE were 2374 and 2665, in OBC these were 3143 and 4089, SC these were 19901 and 21670 respectively.
The course fee is about 1,37,500+30,000 per year.

Hi,If you are not interested in engineering, check and pursue whatever really interests you. It will help you grow very well. For instance, business administration, business management, Bachelors of sciences in various combinations are a few to name.

Well, it has not been so far. So you should wait and see.

Hi,
Well, about the management quota. The best way to approach would be to talk in person with the college authorities. Set up an appointment through phone and talk to them in person. The possibility of getting a seat varies depending on vacancy, which course etc. Start the discussions early on, is my opinion.

Well, both the colleges have lot of such opportunities. Personally, since I have been to many fests and workshops like UTSAV and technical conferences, BMSCE definitely has quite much.

Well, it is important and recommended to write an entrance exam. However, through management quota you will be exempted from participating in the normal counselling process for obtaining a seat. So, you won't really be competing for a seat through cut offs.