Colleges in Jaipur

Yes, chances are there to get. If not just go for more counselings and get admission in particular college for the particular subject.You can easily get MNIT as you have scored good marks which makes you eligible for it.

Yes, there is HRM specialisation available and along with it you can opt for one more specialisation as it is dual specialised course.

You may refer-
https://www.mjrpuniversity.ac.in/how-to-apply.html.

I would not recommend Taxila Business School but Jaipuria, Noida and BIMTECH are at the same level.

You need to have passed class 12th with 50% marks for admission in Diploma fashion design.

I am not sure about it as I am from a different stream but to help you out I am giving you the phone number of food science department below:
Prof. Sheel Sharma(Food Science & Nutrition) Phone: 01438-228341, Extn. 336.
You can contact her any time between 9AM - 4PM, except Tuesday.
Please do check once. Thank you.

Fingers crossed. You have a chance. I won't say the top NIT but getting a NIT has a high probability.