Filing of an I-130 does not allow you to stay on legally until you get legal status. Sibling petitions take many years and with your order of removal, you would not just be allowed to adjust status even with an approved I-130 and visa availability. You would have to get your case reopened. You need to retain a lawyer to assist you.
She cannot come back on a visitor's visa because of the intent issue. You may have to consular process her in as an LPR. Get the I-130 filed and mark "consular processing requested". For heaven's sake, hire a lawyer to do it right. If you had a lawyer to do what you just did, get a different one!
The new H1 will take effect October 1, 2012 (unless yours is cap-exempt). Your H must be filed as a Change of Status while you were here on the B to be able to "convert"; but if that were the case and you left while the COS was pending, you would have a problem. If your H has been filed as consular processing in, then you would have to leave the U.S. after entry as a B and get the H1B visa stamp. You cannot come to the US for that visa stamp -- there is no U.S. Consulate in the U.S. But you...
If you are a U.S. citizen, you need to marry him (you can do so in Mexico) and then petition for an I-130 IR petition. When it is approved, he will have to consular process with a 601 waiver claiming extreme hardship to his USC spouse and permission to reenter the U.S. pursuant to deportation/removal. You should hire a lawyer to help you with all this.
The University is the same sponsor. You should check your DS 2019 and see if it limits you to the department. What does your "actual boss" mean by canceling your "actual" J1? Have you talked to the University's ISO? You need to speak with them -- they can advise you more specifically.
You are allowed to file concurrent H1B petitions -- 2 employers for 2 H1B concurrent positions. But yours does not sound like "concurrent" was checked off on the petition. You can always change an employer but doing it the way you are doing it -- you're going to burn some bridges. Anyway, once the change of employer petition is approved, the extension essentially would be abandoned by you. Do you intend to tell the employer who filed the extension once the transfer petition is approved? --...
Have the employer give you a verification letter that states the name change as acquisition/successor-in-interest. You should not have an issue. If there is a press release to the effect, carry a copy of that as well for back-up. I really don't think you will have a problem with a letter from the employer.