B.Tech Eligibility

You must have a combination of PCM/PCB in class 12th.

A Valid JEE score is must.

An airline company will never hire cabin crew with visible tattoos. Furthermore, there are companies that completely prohibit the presence of tattoos, no matter what area of the body they are located in. Generally, the policy says that no cabin crew can have visible distinctive mark (tattoos, scars, birthmarks).
If you can remove your tattoo then you will be eligible.

Usually, the margin is around 3 years, but you can recheck it this year in November when the forms of the colleges arrive.

For getting into the B.Tech in CSE branch, you should have qualified your 12th class in Science stream with minimum of 50% marks in boards exam and for being in NITs and IITs, you should have got minimum 75% marks in boards exam.

Yes, you can write DCET.

Yes, Maths Students are eligible for any B.Tech course. Dairy Technology at first may seem like a course for Biology students, but it is also for Maths students. The course is aimed more on technology part than the dairy.

You are basically asking about IIT. IIT doesn't provide lateral admission and not even regular admission through management quota. Your Diploma is however eligible for admission into mining engineering. I would suggest pursuing the course from another college.

Firstly their is no fixed eligibility for placement during campus interview as it differs from company to company.The minimum requirement is you should pass with first class in all exams and your attendance should be at least 75% then you get selected by the college for campus selection. Hope this will help you.
Good Luck!

Which course are you interested in?