Q1 Visa in Shenzhen

I was married in 2002 and have young Chinese born daughter from Chinese national mother at 14 years old now, but this year I divorced, and the ex wife moved to Europe so i'm the one looking after the daughter now here in China, my question is can I get a longer Q1 type? I have been here in China since 1998.
next question is if so can I get my Q2 type which expire soon converted to Q1 without leaving Shenzhen?