JEE

Yes, you can apply for this campus. This score is enough for admission in this campus.

KJ Somaiya followed by Rizvi, Spit, DJ Sanghvi, Thakur, Francis and Thadomal.

Sinhgad is the best option as compared to Shri Ram Institute. This Sinhgad has good teaching and non-teaching faculty members. Also, the placement package given by the college is also above 3 LPA for a fresher.

Sorry, it's a bit difficult. If you apply through management seat, you will definitely get it. If it is a government seat, it's too difficult with this rank.

Yes, but you have to write Karnataka State Entrance exam for Engineering then you can avail a seat in the campuses of Bangalore. Also, some private deemed campuses also provide seats without an entrance exam.

Click on the link and watch the video till the end to get an idea about how to find the probable list of colleges you might get on the basis of your rank:
https://youtu.be/hOlit6Un7l0

I think, NATA score is needed for the same.

No, you can't. They offer admission through NATA.

For qualifying JEE Mains (which means to be eligible for JEE Advanced) the minimum marks are as follows:
IN 2018:
Common Rank List - 74
OBC-NCL - 45
SC - 29
ST -24
IN 2017
Common Rank List-81
OBC-NCL- 49
SC - 32
ST - 27
Cutoffs for admissions in various NITs, IIITs, are available at:
https://josaa.nic.in/josaaorcrarchieve/Result/OpeningClosingRankArchieveN.aspx?Year=2017
Here you can see the cutoff's ranks for various categories.