Tell your mom to relax, stay at home in Singapore, you are a big boy now!
She should be fine if she flies in an out of China. I had a Singaporean friend stay with me for almost 2 years who kept ducking in and out of China.
Check your PM. Sent you a link to a private Singaporean group (for Singaporeans) in HK which you might find useful.
Not sure actually. My in-laws hold a Dutch passport and have been flying in and out of HK countless times and staying for extended periods of time for several years. Not sure if ImD would be more difficult with a Singapore passport holder though.
There was a case a year ago about a Singaporean women who lost all her savings in China. She was living in HK as a McRefugee, and making a living as a parallel trader. So I guess it would be ok for OP's mom.
I believe that Singapore passport holders do not require a Chinese visa to visit China. Nor do Chinese need a S'pore visa to visit S'pore.
So, mum can simply pop over to Shenzhen for a few hours, then back to HK even same day, and get another 90 stamp. Probably can do this for years on end.