Bachelors

Yes; after completing your 10th with minimum 45%, you can do Diploma in any field. And after completing your Diploma, you can do any degree course in any college.

Good to see that you want to complete your graduation. You can check out some night school in your vicinity. Also, now a days there are a lot of distance learning programs available. You need not leave your job for them. You can study part time and work too. Check out courses offered by IGNOU.
All the best!

LA Trobe University
UTS, University of Technology, Sydney
University of Wollongong
University of Southern Queensland
Curtin University
Swinburne University of Technology
UTAS (University of Tansamia)

For mass communication, both are good, bachelor's as well as Master's. But, it's preferable that you must complete your Bachelors from India and then you can continue your studies I.e. Master abroad.

Yes, you can retake admission for your UG course. The admission will be based on a personal interview wherein your aptitude for the course will be determined. And you can't say that the college is best for this course, but a fine one.

Yes, of course, you can. You need to clear English proficiency test i.e. IELTS for that and the required band set by the particular university in which you are interested.

Refer this link for admission process of IGNOU : https://www.shiksha.com/university/ignou-indira-gandhi-national-open-university-delhi-3030/admission.

Please specify the college/institute name.

No, they do not offer a sport Science course.