Though you are already given answer on your question, but let me tell you one more time. Once a green card is granted (approval of I-485) whether for conditional green card or unconditional green card, all the disturbing issues become completely MUTE (they don't matter anymore), such as overstaying and working without INS permission in the past, violation of other immigration laws, etc. So obviously, 3/10 yrs bar does get out of the picture completely, once for good.
Further, once an alien's application for Adjustment of Status has already been approved, s/he will not be granted for an Advance Parole. Because Advance Parole is granted for those who have pending I-485, and not for those whose I-485 has already been adjudicated. Besides, why a person would even try to obtain AP if his/her I-485 has already been approved? No brainer. However, an alien must need to obtain a Reentry Permit if s/he would believe that s/he would be out of the country more than a year despite of being a green card holder.