Republic of India/Bhaarat Ganaraajya should be written as भारत गणराज्य. Or you could just have भारत (Bhaarat) because you didn't ask for the official name of other countries.
I was quite unsure about that one as I know India has many languages which use multiple different scripts. Would the devanagari script be used nation wide or would the romanised spelling be more commonly used? Wikipedia just provides the romanised spelling so I assumed that would be what is most commonly used.
Devanagari is widely used for various languages as well as Hindi (though of course there are other scripts in use. Also some languages can be written in either Devanagari and another script, like Persian-Arabic). The Latin alphabet is usually used for English, so I think the Devanagari spelling would be the most appropriate here.