Getting H1b before joining date

[Kabira]

I am currently working as a postdoc at a university on F-1 OPT that expires in Jul 2015. I can not leave my postdoctoral project until Sep 2015. My question is that
1)whether it is possible that I get an offer letter from industry (hopefully by Jan-Feb 15) and let them process my H1b while staying at University on OPT?
2) According to information I have, if they file H1 on Apr1 and get approval I will have to join them in less than six months, is it correct?
3) This means that I will have to start applying for jobs by dec 2014, is it too early, or companies do realize these scenarios?

I am eligible for STEM extension but don't want to waste one chance of getting H1b.

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