1. 母親在美身份超期滯留已經超過兩年，這種情況下是不是就算申請到了回美證也不能離開美國?
-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. 父親在國內查出癌症，能否從人道角度出發申請綠卡加急？
-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，母親一旦回到中國就有可能10年孤身一人見不到子女 - 現在中國政府基本不批準探親簽證。
