1. Yes, your grace period is what we spoke about in our last email, just not by name. I understand it's confusing to travel with an I-20 that looks expired (after the program end date), but page 2 of your new I-20 will show the OPT request, and your OPT receipt notice will be proof that you have an application pending with USCIS. So, this proof makes it okay to travel during this time. (USCIS will not abandon your OPT application if you travel abroad while it's pending.)
2. I have not heard of this happening--you should be fine. Students on OPT are allowed to have up to 90 days of unemployment, so you should not be penalized unless you have gone over that limit.
3. This is similar to the answer in question 1--it's strange to travel with an 'expired' I-20, but the OPT notation makes it okay! The I-20's program end date has to remain Dec. 2015, since that is when you finish your degree program.
it is ok/.//
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