Can I work while studying at the University of Tokyo?

To enroll at UTokyo you need to meet the eligibility requirements of the Japanese education system. As per it, student to have spent 16 years in schooling to enroll in a Masters degree and 18 years for PhD. If you don't meet the requirement refer to official website of University of Tokyo and follow

While not mandatory, GRE scores are strongly recommended for some graduate programs at the University of Tokyo. Each course can have a different policy on GRE test scores so check the same before applying

Yes University of Tokyo acceptance rate stands around 36 % meaning out of every 100 candidates who apply upto 36 will  be accepted. This makes it hard to get into the university as little over one fifth of applicants will be admitted

No students cant apply to more than one programme at Univeristy of Tokyo. If you want to apply to a programme froma notehr department you should withdraw your current application 

Yes even if you don't have valid passport and youre worried about what to write in field of passport name you can write your officially registered name registered in census register or provide some other proof of citizenship for India to Univeristy of Tokyo.