CPT

Not necessarily, but for knowledge, you can pursue it if you are free for a month or two.

Paper I: Principles and Practices of Accounting (100 Marks)
Paper 2: Mercantile Law & General English (100 Marks)
Part I: Mercantile Law (60 Marks)
Part II: General English (40 Marks)
Paper 3*: Business Mathematics and Logical Reasoning & Statistics (100 Marks)
Part I: Business Mathematics and Logical Reasoning (60 Marks)
Part II: Statistics (40 Marks)
Paper 4*: Business Economics & Business and Commercial Knowledge (100 Marks)
Part I: Business Economics (60 Marks)
Part II: Business and Commercial Knowledge (40 Marks)
*Paper 3 and Paper 4 will be Objective type papers

Hi Arwinder,
You cannot study in two countries simultaneously. You can do your B.Com abroad through online or distance and do your CA here. Check here for college list
https://www.shiksha.com/accounting-commerce/colleges/b-com-colleges-india

Kindly refer to the link mentioned below:
https://goo.gl/G35eCN

Both the exams have their own importance in their respective field. You can't compare CPT or CLAT because these entrance exam will take you to two different professional courses.
CPT is the entrance exam to become a chartered accountant whereas CLAT is the entrance exam for different careers in legal field.
Thus, decide what you want to do and for further queries feel free to revert back.

After clearing CPT, you can directly register for CS Executive, but if you want to pursue CMA, you need to crack its foundation. If you don't want to give CMA foundation, then you need to clear IPCC and you will be eligible for the exemption of CMA foundation.