Well, for starters, we can't say how long you will last financially since we don't know how much money you have saved.
Second, it is well known that many Indians here are working in the IT industry. The more Japanese language skills you have, the better. Expect to be paid unfairly low wages. How much work experience do you have? A lot also depends on whether that is in an area that the Japanese needs, otherwise they'll just hire a local who can speak the language and get along with the work culture.
I don't think martial arts schools are eligible to provide sponsorship for student visas.
Monthly expenditures will vary, but on average think of this:
rent 50,000-80,000 yen
utilities 10,000-15,000
food 40,000-60,000
phone/internet 10,000 installation for cell phone, then 3500-8000 per month
insurance 2,500 the first year then tenfold higher after that
Transportation is often/usually paid by the employer, but find out in advance. Otherwise, expect roughly 25,000 yen.