H1B 6 years cap expiring in 12 months, Is it possible to apply GC now?

USA H1B Visa
1

Hi Saurabh,

 I am completing my 6 years cap in jan-2015. I got the visa stamped in sep 2012. But i switched my job a month back. Now H1b is valid till Oct-2014 only. But I-94 is til Jan -2015. My queries are

  1. Is it possible for my new employer to file for labor immediately? Does the 365 day cap affect me?

  2. What would be other options for me to stay in US without leaving the country?

  3. Is it possible for a US citizen (my niece) to sponsor Greencard for me? Or does this 365 day rule apply there as well?

Please help me get a clarity.

Thank u very much in advance.