H1B denied another employer ready to sponsor FY2013

I graduated with MBA in 2011 and I had my OPT valid from Oct 1st 2011-Oct 2nd 2012. My employer filed H1B visa which got denied on 26th Oct 2012 and since my OPT expired I had to cease working. My employer filed for MTR on Nov 7th 2012. Here are my questions: 


1. Since I was eligible for an automatic cap-gap extension of status and employment authorization, but my H-1B petition got denied, am I allowed for the 60-day grace period from the denial date to depart US? Or do I need to depart 60 days from the EAD expiry date? 

2. I have another employer who is interested to hire me. Can they file for a new H1B visa petition this year or it can be only filed in April 2013?
  1. From your Denial date I believe, but check with you school DSO to confirm how officially they count the days.

  2. If this is your first H1, you can only file in April 2013 not before that.

But if the amployer is NGO, research institution/ University they do not go under cap and are allowed to apply for H1 all through the year.