Generally, if you resign from your L-1B employment, you are no longer in a lawful non-immigrant status. You will start incurring unlawful presence which may have adverse consequences. Also, a change of status request cannot be approved if you are not maintaining your current non-immigrant status. Please hire a qualified immigration lawyer.
1) No. I-94 states period of authorized stay. Once terminated, you status ends.
3 & 4) Once status expires, you should ideally leave or talk to a competent immigration attorney to consider if a nunc pro tunc employer petition can be filed in your behalf.
This response is general in nature and cannot be construed as legal advice, given that not enough facts are known. Any comments offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship. If you would like additional information based on this response, please contact my office at 510 657 7665 or 415 902 0832 to schedule a consultation.