You definitely need to speak to an immigration attorney about the specifics of this case. The answer depends on a number of factors, including when your son was admitted to the U.S. (specifically, if he was admitted within the last five years), the maximum sentence that may be imposed under the specific criminal statutes, and (potentially) whether the two sentences came from the same incident. If he was admitted to the U.S. more than five years ago, and the two convictions came from the same incident, he is potentially fine to travel; however, I cannot stress enough that you or your son should speak to an immigration attorney regarding the specifics of the case.See question
I think the heart of your question is whether you can still pursue asylum after your divorce. The short answer is yes, you will be able to pursue the asylum. However, you will probably need to sever your case from your wife's case. You (or your attorney) could file a "motion for severance" with the Court. You'll want to do that long before your hearing date. It sounds like your claim is a religion-based claim, so as long as you hold those religious belief (or as your persecutors would impute those beliefs to you), you should still be able to pursue the claim.See question
I think your question boils down to whether you can apply to asylum even with a prior deported. Prior deportations usually do not prevent someone from seeking asylum. The main exception is if the criminal activity that got you deported in the first place triggers one of the bars for asylum. Also, you will be unable to apply for asylum if you have already applied for asylum in the past (unless the circumstances have changed that would materially affect your case).
So, unless one of those exceptions apply, you should still be able to apply for asylum. You'll have to meet all the other requirements though, which are many (keep an eye on the requirement to apply within one year of your last arrival to the U.S.).See question