Programming

In 20 days, you can only brush up the basic part in Java, learning any language completely is not possible in just 20 days, but I would recommend you to go ahead and learn as much as you can in 20 days and then sneak out few hours on a weekly basis to master Java.

Programming is a combination of technical knowledge and what creative you can do with that knowledge, hence it can never be based on any syllabus whether its a college syllabus or any other syllabus, you must have the logical and analytical approach in whichever language you study.

NICT Computer Education
NIIT
ICIT
NIVT (Novel Institute of Vocational Training)
Aptech Computer Education
are the best institutions for computer programming.

CETPA, CPD Technology are some of the best training institutes for PHP in Delhi-NCR.

Opt for the course that you love the most and are most passionate about and analyze the future work conditions, scope and growth prospects before taking admission
You can also opt for psychometric test comprising of aptitude, personality and career interest to clear confusion

Yes, there is a provision for completing MBA under specific conditions in IGNOU. You can contact the admission cell and understand the conditions applicable for it.

There is no eligibility as such to pursue a Java course, you can pursue a java course even after class 12th or you can pick any good institute in your area to pursue the same.

Yes, you can apply for the Java course, for details check out the article below:
https://www.shiksha.com/it-software/programming/articles/all-about-java-courses-certifications-blogId-5633