1. 母亲在美身份超期滞留已经超过两年，这种情况下是不是就算申请到了回美证也不能离开美国?
-This rule was modified a few years ago specifically for travel using advance parole. It should be fine for your mother to leave US without triggering the 10-year bar if she files I-485 and gets the advance parole and use the afvance parole to travel.
2. 父亲在国内查出癌症，能否从人道角度出发申请绿卡加急？
-No for green card. But your mother may call USCIS to get the emergency advance parole after she files I-485 (with I-131) and get the receipts. She needs to call USCIS ((800) 375-5283) to schedule an appointment to meet with a USCIS adjudicator at a local USCIS field office about the Form I-131 and its accompanying evidence.
See these links:
How to Make an Expedite Request | USCIS
How to Expedite the Processing of I-131 Travel Document? | DYgreencard
如果不能加急，母亲一旦回到中国就有可能10年孤身一人见不到子女 - 现在中国政府基本不批准探亲签证。
