Can I go for CA, CS and LLB together (if I go for a dummy internship in CA & CS both of 3.5 years and 15 months respectively)?

All these three courses are extremely demanding, it is better to pursue the same separately as you would not be able to cover the same together.

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.