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Here are two things to keep in mind:
The problem reading time must be reduced. You should be able to read a question and translate it into variables and/or diagram/equation at one shot. Most students read a question slow/multiple times with an intrinsic fear of getting it wrong otherwise. Practice reading fast. We seldom realize that toppers save half the time in reading and understanding the questions faster than others. The problem solving time can be reduced. Conceptual/process memory builds if you have solved different types of questions multiple number of times. I suggest a student should revise his/her coaching books/sheets at least 3 times before CAT. Look at CAT teachers, they solve questions so many times that the types become very clear to them and the solving process comes naturally to them. The difference lies in the process memory. I have solved questions so many times that I can think faster and solve faster than before. A student can become up to 100% faster than before by practicing limited content (which includes problem variety) multiple number of times. Most students find this re solving boring and ignore it. You must not do that. Revise!
Learn fast track tools: basic mental multiplication techniques, squares, fractions and approximation techniques (based on trend analysis in the numerator/denominator). Learn how to structure constraints in LR; learn methods for syllogism; practice 34 variable sets and matrix formation. Knowing these techniques saves time. Give lots of timed tests: Speed tests/sectional tests/topic tests - I would say: at least 50 such tests per section must be taken. Helps you manage hormones in the exam hall - teaches you to focus hard in a short span of time (normally such tests are 20 minutes to 60 minutes in duration). With practice, you become skilled to sit for 3 hours with full focus and speed.

After getting a good percentile in CAT, the IIMs where you have applied looks at your profile, and they judge you on the basis of your class 10th, class 12th, undergraduate, CGPA marks. Weightage given to CAT is around 30-50%. Based on an overall score and CAT score, you may be called for a personal Interview, after which the deciding factor in selection will be mostly the interview performance. Also, you will start getting calls from different MBA colleges for their interview process. You have to shortlist the colleges accordingly, and then appear for the GDPI session for the college. If you pass the GDPI selection process, you are through to the college.

The CAT exam comprises of 3 sections and you are given strictly 1 hour for each section. Therefore there is no question of dividing time across sections. However, if you are enquiring about dividing time within each section, then I would suggest that it is important to divide equal time to all parts of the section and not miss out on say the last few questions of the paper because you took more time initially. If you do not get an answer or approach to a problem within a minute, its better to move on. Now coming to the scoring section part. Yes in absolute terms, there is disparity in terms of scores across sections. People who are strong at quant generally score very high in the section and those with good familiarity with English do well in the RC section. However, the LRDI section has been tough and low scoring over the past few years. Therefore, it is often this section that separates the well prepared and smart candidates from the rest of the pool. Therefore, I suggest that one gives a lot of time to getting better in this section.