What are the requirements to open a Demat account for trading? Can an NRI open a Demat account and if so, what are the restrictions?

NRIs can open Demat accounts. NRIs from middle east can do online trading through icicidirect.com as well.

Here is information about opening a Demat a/c for a resident - http://www.idbibank.com/products/demataccount.asp

Special conditions for NRIs - http://www.idbibank.com/products/demataccount_nrispecialconditions.asp

----------RBI permission is needed to trade in non-IPO (secondary market) securities.

 A useful FAQ on that - https://nsdl.co.in/downloadables/faqonnris.doc

Thanks,

Rupali