That should not be a problem since it has been over 10 years that he departed from the US. He probably will not have an issue, but it is advisable to discuss the details of his case with an expert attorney because there are always certain nuances that cannot be fully addressed in a brief response.
Your case is certainly one where a mandamus action seems to be the best option. As for time frames, attorneys fees, etc, you can contact us for details. I find that mandamus is indeed the best way to resolve long-delayed adjustment cases, particularly if you have a bona fide (genuine) marriage that may be under investigation for some reason.
What type of petitioner (sibling, spouse, parent, child, etc...) and what was his status when he or she passed away (permanent resident or U.S. citizen)? Also, it depends if you were in the U.S. when the petitioner passed away. As of 2009, there is a new section of the Immigration and Nationality Act [Section 204(l)]. We have done many motions to reopen an I-130 under this subsection and all of them were granted promptly by USCIS. You may contact our office for more details.
You definitely need to consult with an experienced attorney ASAP. If his priors were as a juvenile, it should not be a problem generally speaking (with a few exceptions) in terms of bond eligibility or removability. However, if his priors took place when he was over 18, an attorney must review in detail the criminal history to see if he is bond eligible or subject to mandatory detention and if relief is available to him, such as adjustment of status with or without a 212(i) (I-601) waiver, etc.
It depends on what happened each time she was caught and what bars are placed on her because this is a very complex area of law. Yes, a waiver (request for "forgiveness") is available in certain cases, but to be sure if it is available in your mother's situation, you should consult with a knowledgeable, experienced immigration attorney. We can help determine if a waiver is even needed and if one is available and the likelihood of success in your case during a more detailed consultation.
Yes that should be sufficient. Notify the asylum office directly as well by mailing in a change of address form aside from filing out the AR-11 online COA form and for a pending I-589 as well through the USCIS website.