IIT

There are some good institutes apart from IITs, NITs and IIITs. You can check this list:
https://www.shiksha.com/b-tech/ranking/top-engineering-colleges-in-india/44-2-0-0-0. This list also includes IITs, NITs and IIITs. So, I will mention the colleges other than IITs, NITs and IIITs here:
BITS-Pilani
I

Sure, you can. 5 months is a long time, you can join some good crash course of 3 months to align yourself for IIT Advanced and devote 2 remaining months for mock exams and practice.

Yes, you can. All you have to do is clear JEE Mains and your ranking should be under 20000.

Please refer to the link provided below for details on IIT JAM entrance exam for M.Sc. courses in the IITs. You will get important dates related to the exam, syllabus, exam preparation tips, important news related to the exam.
https://www.shiksha.com/science/exams/iit-jam

Number of seats for students appearing for IIT JAM (Course in M.Sc. in Statistics) are as follows:
1) General-25
2) OBC-14
3) SC-7
4) ST-4
5) PwD-1
Total number of seats-51

There are lot of colleges, which is good apart from IIT.
These are:VIT University,BITS Pilani,KIIT University,Satyabhama University,
SRM University,Sastra University,
Thapar University,BIT Mesra,Jadavpur College of Engineering,Jaypee College of Engineering,Galgotias University.

Books For IIT JAM Physics:
Mathematical Methods : Paul Goldbarts
Mechanics and General Properties of Matter:JAM - Physics (2019)
Oscillations, Waves and Optics
Electricity and Magnetism: James Clerk Maxwell
Kinetic theory, Thermodynamics: Stephen and Katherine Blundell
Modern Physics: Kenneth S. Krane
Soli

There are two exams.
1st is JEE Mains and another is JEE Advanced.
After qualifying Mains, you are eligible for JEE Advanced and if you qualify Advanced, you can get admission in IIT on the basis of your rank.

Hello Sunil,
There is no particular cut-off score, instead, you will be having closing and opening ranks for each IIT that vary every year.
Also, the marks for each JEE Advanced paper are not fixed.
For getting admission into top IITs, your all India rank should be at least below 4000.
All the best.