Mumbai

Thakur College does not offer part-time MCA, check out the link below for details :
https://www.shiksha.com/college/thakur-college-of-engineering-and-technology-kandivali-east-mumbai-47539

Sikkim Manipal will be a better university as compared to Mumbai University for distance BCA.

You are required to visit www.ricssbe.org and click on apply now link. We look forward to receiving your application. You can also download our brochure online, the E-brochure will provide you all the details that you need pertaining to the programs and to complete the application process. The last date to submit your application is 31st August and the entrance is scheduled on 1st September 2017 at Mumbai campus.

SPJIMR is one of the top B-Schools of India which offers a multitude of programs for all those who want to gain quality management education.
Please refer to the following link for details of hostel and course fee:
http://www.spjimr.org/pgdm/admissions/india#node-256

https://www.google.co.in/url?sa=t&source=web&rct=j&url=http://www.iismworld.com/&ved=0ahUKEwiQlO_m-fzVAhWIqo8KHaYqCdYQFgiEATAD&usg=AFQjCNEIDKKsisD3XqkvOD2HGi1YQt1G0g
This college provides degree in Sports Management.

For Law, LLM at ILS Law College.

Yes, you can.
First, you should have a valid Indian passport and they have certain eligibility criteria, for that, you should check their website.