I-797/H-1B Visa/I-94 expiring in Aug 2016 and Passport in Dec 2016


I’m on H-1B Visa which is valid till August 2016. My I-797(H-1B Petition)/H-1B Stamped Visa and I-94 entry will expire in August 2016 and my passport will expire in Dec 2016.

As per my understanding, I can apply for my passport re-issue one year before expiry, so will apply for the same in Dec 2015/Jan 2016.

Now, I am thinking about joining another company and my new employer will file for H-1B transfer and extension. So, my doubt is that whether my H-1B extension will be till the my passport expiry date or beyond that?
Also, In case, i change my employer and my visa expires in Aug 2016; can i stay in US legally post that or will have to travel back to India to get my visa stamped and then return back?

Kindly help me in clearing out my doubts.