NIT

A 96 percentile in JEE Mains will put you in the general percentage of score between 33000 and 48000. The score is not enough to get an admission in best IITs or most popular faculty members (such as CSE ) in best NITs. But you can easily get into mid-tier NITs (e.g. NIT Agartala, NIT Raipur, NIT SIlchar, NIT Srinagar) in core subjects such as Civil, Mechanical, Chemical, or even Metallurgy. You may even secure a place in newer (e.g. IIIT Manipur, IIIT Bhagalpur, IIIT Dharwad) institutes to other branches such as ECE. This is also dependent on your category and quota of home state.

Yes, it is possible to get into some NITs with a GATE score of 395 and AIR 1217, especially if you are from a reserved category or are open to less competitive branches or specializations. While the chances of getting into top NITs or highly sought-after specializations are slim, there are NITs with lower cutoffs where admission is possible with this score.

With a JEE Mains rank of 25,000, you have a good chance of getting into some NITs for Computer Science Engineering (CSE) or Electronics and Communication Engineering (ECE), particularly at the newer or less popular campuses. You might be able to secure a seat in CSE at NITs like NIT Jalandhar, NIT Uttarakhand, or NIT Sikkim. For ECE, you could potentially get into NITs like NIT Calicut, NIT Bhopal, or NIT Surat. However, getting into the top NITs (Trichy, Warangal, Surathkal) for CSE with this rank would be very challenging, although ECE might be a possibility in some of them. 

He can try for the branches other than CSE and ECE in low range. You can likely get into some IIITs but not the top one's. The specific IIITs available will depend on the category branch and the overall seat availability.

With a JEE Main score of 96.6, securing a seat in the top NITs for Computer Science (CS), Data Science, or AI is hard. In NITs like NIT Srinagar, NIT Jalandhar, NIT Bhopal, and NIT Patna might be possibilities of lower Branch like civil, chemical, if you have a good rank within your category of ST SC you'll get higher branch like computer branch.

Your NTA score is 20.8 means your estimate rank is above 5 Lacs, so it's very unlikely for you to get admission in NIT, until you are from ST category, but you can go for a private college that accepts on the basis of 12th class or management quota.

Yes, Mechatronics is good in VIT Vellore as it involves a modern curriculum, strong labs and research, good faculty, and industry exposure. Mechatromics is equally good, I'm IIT, NIT with slight differences.