a). Although you entered the United States on advance parole this time you are still considered to be holding a H-1B status. That is not disturbed by your exit and entry.
b). The I-94 that you get with the advance parole entry is limited and hence it should not be a problem. You should be able to transfer employers. You definitely can amend or even extend your H-1B within the United States. I am not aware of any limitations on the ability to use the H-1B for a transfer.
c). Yes you can always revive an H-1B. If the H-1B has expired, you can seek a renewal of the H-1B through the USCIS and then go outside the USA (your home country or any country) and get a H-1B visa stamp and come back.
Note: Where transcribed from audio/video, this is a verbatim transcript of the referenced audio/video media delivered as oral communication, and, therefore, may not conform to written grammatical or syntactical form.