Diploma

For the fee structure of this course, you have to visit different colleges/university websites because the fee structure is different in each college.

Yes, you can definitely apply for DTU lateral entry exam. Best of luck for your future and if any query feel free to ask.

Please check for your eligibility to pursue B.E. in Mechanical Engineering from D.Y. Patil College of Engineering from the criteria mentioned at the link provided below. Admission process followed for this course is mentioned at the link provided below:
https://www.shiksha.com/b-tech/course/b-e-in-mechanical-engineering-d-y-patil-college-of-engineering-akurdi-pune-157239

Better to go for MBA entrance exams, prepare well for the exams. A good score in CAT and similar entrance exams will help you to get into top B-Schools. One of the top institute for Digital Marketing is MICA. Other institutes like Iims have marketing as the specialisation and digital marketing is part of that, you can still get into digital marketing profile.

If you have proper reason for how you utilised the gap period, whether you joined any organisation for work, working on any research paper/ project, preparing for entrance exams. You need to properly justify the reason. Also if the gap period is of 1 year than it is fine, generally gap of more than 1 year is questioned.

Yes, you can. Diploma is based on your 12th and 10th mark. So, if you have successfully completed both 10th and 12th then you can apply for Diploma.

Check the below link for colleges-
https://www.shiksha.com/banking-finance-insurance/colleges/diploma-courses-Bangalore
You can look for colleges based on ranking, fees, placement, courses, placements, accreditation, admission details, brochure, infrastructure and location.

After completing B.Tech, I don't think Diploma in hotel management will be good idea. Now, the fees varies from college to college.