1. Yes, you can apply while the appeal is pending.
2. Yes, you must make sure you do not have gaps in your status, so do be careful to apply in time to extend the H-4 before it expires.
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You asked this quesiton before. yes, but will have to go through a consulate. You will be CAP subject.
NYC EXPERIENCED IMMIGRATION ATTORNEYS www.myattorneyusa.com; email: email@example.com; Phone: (866) 456-8654; Fax: 212-964-0440; Cell: 212-202-0325. The information contained in this answer is provided for informational purposes only, and should not be construed as legal advice on any subject matter.
An employer can file a petition. For USCIS to change your status, you must be in status on September 30th. Otherwise, you will need to obtain an H-1B visa stamp abroad after the petition is approved and before you can begin work.
Your employer needs to retain an experienced immigration lawyer to review all the facts, advise them, and handle the case. Your employer can find one through http://www.ailalawyer.com.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.