Do you have a potential employer in mind ... or are you just exploring your options?
Simply put, it is never a good idea to change employers while papers are 'in the works'.
Other questions would be best discussed in private, with a different lawyer than the one that works for your employer.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Visa is for travel, it is not proof of your status. Regarding changing employers, I strongly recommend not to file multiple petitions simultaneously as they can create confusion especially if they are filed as change of status petitions seeking a particular date when the status automatically changes. Speak to a competent immigration attorney to discuss your options.
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 to schedule a consultation.