Will I need a carte de sejour vie privee et famille?

I’m from India and I’m currently doing my masters in International Business in Grenoble. The academic part of this course ends in the end of May. I plan to launch a web startup which is going to be a service, for which I feel the best market is here in France. I leave back for India at the end of May to develop this website and I intend to come back to France once the website development is complete, estimately around September and launch the website here.

1. What is the procedure for me to register this website in France?
2. Can I do this online?
3. If I register my company in France, what implications would it have?
4. Would I have to set up a workplace in France only or could I do it from another country?
5. Can I choose to register my company with another country and still launch my website here in France?
6. If I have logos and slogans as part of my website, how could I register the trademarks?
7. If the website had a new business process, is there a way I can register a patent on the whole business process?
8. If I leave France now and let my carte de sejour (etudiant) expire, would it be possible for me to extend my visa/ get a titre de sejour on the basis that I’m going to start a company in France, if so what is this visa called?
9. My venture would possibly create some jobs in France are there any benefits I could receive due to this?