You got your GC through your mother after the appropriate waivers. Will you be asked about it. We cannot be sure, but with immigration they can ask just anything. Will it be a problem about your past asylum case. I highly doubt it will be an issue, as you followed the proper steps after that.
As for your marriage, yes they can ask but as you did not get any immigration benefits from that marriage. They probably won't ask other then to check your legal marriage status. Which you would show your divorce decree. Again it will not harm your case.