Income tax for nri with indian income

Dear sir,

I am NRI having some queries below. Please some expert advise me.

1. Is it compulsory to file ITR even without Indian income?

2. I have some Indian income from...

a) house rent

b) short term capital gains mainly from sale of shares

 c) speculative trading in F&O.

how are these incomes  to be  shown in ITR and at what % tax is to be applied?

3. Can I fill ITR & pay the income tax online through IT website without submitting hardcopy?

4. If it can be done, how is proof of income submitted?

Thanks

tvrao