How would you rate the following colleges- BIM Trichy, LIBA and IFMR?

Three months may not be enough for CMAT preparation, if you're doing it from scratch. However, if you are preparing for CAT, XAT, NMAT, you can prepare for CMAT in 3 months as you have clear understanding of the syllabus already and you will need exam specific practice only.

No, candidates are not required to appear in CMAT to be eligible for BTech in CSE + MBA integated course at UIT, Karnavati University. For this course, candidates are required to appear in either JEE Mains or GUJCET to qualify for admissions.

If you have appeared for CMAT before and have complete conceptual clarity of topics, you can prepare for CMAT with mock test practice only.

For CMAT English preparation, candidates can refer to High School English Grammar by Wren and Martin and Word Power Made Easy by Norman Lewis. These two will help in building grammar and vocabulary.

Manorama Year Book, Lucent's General Knowledge will be a good source to prepare static GK for CMAT. Apart from that, you should refer Pratiyogita Darpan and GK Today for current affairs.