An:
1. Can apply from travel agent in Singapore. 4 working days. Single entry for your mum. But Malaysia embassy got the right to reject her Visa, it is case by case. One more choise, apply Visa on arrival at 2nd link level 2 office. Need to bring passport, return tickets, and RM100. Spend 5 mins only.
2. Not sure.
3. Nowadays, S'pore Visa is usually 2 years multi-entry (or even 5 years, depends on your luck :D ). Max. stay 14 to 30 days (refer to the stamp on her passport when enter S'port custom). To Malaysia, 14 days if apply Visa from agent. 30 days if apply Visa on arrival. Both single entry for your mum's case.
4. Yes. 4 working days.
Call any travel agent for more details.