Engineering Entrance Exam

Not more than 50k for general category and that too you will get in last few rounds. For NITs, it is around 25k.

You should be between 3k to 5k to get admission in IHM-Mumbai in 1st round. And for 2nd round, you must be between 5k to 7k. I suggest you to not join IHM-Mumbai or any other hotel management course, better do simple B.Sc.
I am writing this because, I got IHM Mumbai in 2017 in 1st round of counselling, but after reporting IHM Mumbai, my mindset changed by seeing the scenario of the hotel industry and withdrew my documents and seats on the second day after that.
Currently, I am preparing for Engineering competitive exams.

What is your exact question? What kind of guidance do you need? Please be clear.

If internship is of not more than 2 months, surely go for it, it will help you gain good practical knowledge as well as something good to write in your resume. For GATE, I think, if you study well in the rest of the time you have, you will surely crack GATE with good marks.

Placement wise, if you go for new NIT or IIT (new), there is very less scope. I think you take a 1 year break and improve your rank. Then, you can get easily any old IIT.

The following factors will be reviewed by the concerned authorities while preparing the JEE Main cutoff for NIT, Hamirpur. All of the listed factors are related to the JEE Main examination.
1. Cutoff trends of previous years.
2. Total number of candidates for the course.
3. Performance of the candidates in the examination.
4. Difficulty level of the exam.
One needs to take the JEE Mains exam and secure at least 75% marks (65% for SC/ST) in class 12th exam or be in the top 20 percentile in class 12th exam conducted by the respective board. Admissions are on the basis of rank in JEE Mains.

I think, you have to prefer Employment News for that in that you get all the details.

No, you have to give JEE (paper-2) to get admitted in SPA.

Do engineering in the best college of your city and after 4 years, prepare for GATE.

All the courses offered by CUSAT has their own entrance tests except MBA. For MBA, any of the exams like CAT CMAT or KMAT is accepted. The CAT exam conducted for other courses by CUSAT is not applicable for any other universities.