Prof. Rakesh Shrivastava, GIM, Goa

A list of top 10 online coaching is provide by Shiksha on its website!
Checkout the link given!
https://www.google.com/amp/s/www.shiksha.com/mba/articles/amp/top-10-online-mba-coaching-websites-you-should-look-at-blogId-11478.

Hello! Yes, you are partially right, but an MBA from a top-ranked B-school will always remain valuable in the corporate world than one from an average college.

Hello! Yes, it is the best way as all the Iims and some major non-Iims accept its scores for their admission processes. However, there are other exams too like XAT SNAP NMAT, CET, IIFT etc. Which can also get you similar top-ranked colleges. Good luck!
P. S. No reputed college gives direct admission.

Some people find 4-6 months and some 12 months, its depends. But certainly this is largely depends upon person to person.

Identify your strength and weaknesses. Make sure you practice more on your weaknesses more and also do not leave your strengths aside. You keep giving less hours on your strength and more hours on your weaknesses. Also keep on practising model papers and keep time yourself for each section as time is an important factor in CAT.

CAT is the examination for colleges for India. For international studies you should give exams like GMAT for Management studies.

LM Thapar is a good college in north India. I do not know the cut-offs.

For CAT topic: You must identify the section you can improve most in, it is worth the effort. If by Goa you mean Goa Institute of Management, we had 100% placement, the highest salary is of 22L, and average is of 10.5L.