I am a CBSE student who took commerce with math and eco in grade 11 and 12. Am I eligible for B.Sc. Economics course in st. Xaviers Mumbai?

Yes, You are eligible for LLB at Asian Law College if you've scores 80% aggregate in Graduaytion from a recognised university. The minimume eligibility for the programme is having a Bachelor's degree with at least 45% aggregate (40% aggregate for SC/ ST/ OBC). 

Yes, the University of Sydney accepts CBSE marksheet as it is the Central Education board of India and also fully recognised for direct admissions to UG courses at the University of Sydney. 

The most important requirement is to have a high school Diploma equivalent to an Australian year 12 quali

It's difficult but in some colleges you may can get 

Yes, as an Indian student, if someone has completed their class 12th education from CBSE, they can apply for the Westford University College. For UG programs available at this university, the application has to be submitted with the English language proficiency as well. 

Other than this, intern

Generally, no. If you have scored above 75-80% in English in your Class 12th boards (CBSE/ISC), Public Universities in Singapore usually waive the English proficiency requirement. However, for a Master's degree, it is often required unless your undergraduate degree was taught entirely in English.