re;

We didn't submit my I-129 form. I think it is the situation when you submit H1 and H4 at the same time.
I am not sure your second question. I heard that 60 days is grace period, which used for your preparation to leave USA. if you could not find a job now, it is better you submit your application 3 days earlier in case your illegal status...I could not give you other suggestions...you would better consult the lawyer..if I were you, I would not wait after Dec.9th....
as I noticed, it only takes one month to change F1 to H4 in Texas Center..once you find a job, you can easily change from H4 to H1 by premium processing...