LLB

Doing three of them together is quite difficult and unnecessary. Instead, combination of any the above two like CA + CS or CS + LLB is recommended. Most people prefer CS + LLB as it gives full scope in company civil and criminal law.

Law graduates with LLB through distance learning cannot practice in the Indian courts. Corporates prefer practising lawyers as a corporate lawyer. Few corporates might give you job in their law department based on your qualification.

MBA from Nirma University will a good option. They offer 100% placements for MBA and the average package offered is Rs.7.5 lakhs to Rs.9 lakhs.

To get in administrative services, you need to write civil services exam conducted by UPSC. The minimum qualification required to write this exam is that you must be of 21 years of age and you must have a Bachelor's degree.
You must complete your graduation, and then you can apply for civil services exam. You must start your preparation by reading newspapers. Then, you can read class 8th to 10th NCERT books. Slowly, you can catch up with the fundamental books required for UPSC.
All the best.

LLM or CS course will suit you more. You can pursue the same along with your MBA. If you interest is in finance then pursue CA along with your MBA. Any MBA degree will lead you to corporate legal career.

Yes, it is quite possible currently as per the system, you can surely pursue both the courses at the same time in the manner stated.