1) Can't answer this without reviewing the original filing, the RFE, and the proposed response including documentation - you need to consult an attorney directly.
2) You CAN do this, p to the expiration of the L-1B July 12.
3) Depends on the reasons for denial - most likely will just deny saying you don't qualify for L-1A status, not on basis of company interrelationship (which would impact L-1B) or fraud or status violation (which would impact your overall admissibility). IF this is the case, you could still go forward with an L-1B extension; if not, even the L-1B extension may be problematic.
Again, would need to review the specifics of the case to give detailed advice, including pros and cons.
Is there not a retained immigration attorney on the part of the employer? Only they can really answer these questions. Without access to your full file this is not really something we can answer.
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To be honest, the only 'safe' option is to go back home and return to work at the parent company that sent you to the US for this temporary job assignment.
Then, the lawyers can sort things out with immigration without risking you falling out of status and jeopardizing your future.
Talk to an attorney.
Franco Capriotti - Senior Legal Counsel & Former Professor of Immigration Law - Capriotti International Law
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Do not rely completely on information you get on a website. It is always wise to consult personally with an immigration attorney before taking any action.
Consider contacting one of the attorneys on Avvo, or www.ailalawyer.com - If you are low income go here: www.justice.gov/eoir/probono/states.htm or http://www.immigrationlawhelp.org/
FORMER IMMIGRATION LAW PROFESSOR -- LEGAL DISCLAIMER: This answer is offered for informational purposes only. It does not constitute an attorney-client relationship.