1.What is the best way to make google index my new domain ?
Google Webmaster
2.is it okay if it is just duplicate site ?
Content the same? Does it leave the same footprints? Google likes original.
3.what kind of backlinks good for new unindex domain ?
Naturallinks
4.how long until we put backlinks into it ?
Personal preference, but I would say make sure you site is done at least and you have prepared content going out on the regular.
You should really read the forum more as all this is covered in detail. Some of the answers change based on so may variables such as type of site (ecomerce, Ad based, CB, aff and many others. SO DIG DEEP and find the right info)