1. The answer is yes.
2. It depends. Normally 60 days grace period is available for unexpected cessation of employment. As long as your I-94 is valid. But let's say your I-94 is valid for only 45 days you will not get a 60 day grace period. You will get a 45 day grace period. More...
Note: This is a verbatim transcript of the referenced audio/video media delivered as oral communication, and, therefore, may not conform to written grammatical or syntactical form.