professional training from them -- calmly tell her that you will need time to absorb and digest. Like to do the training in a OJT format.
know how to speak English -- As long as work is being communicated (in the same way before I got promoted), it will be fine, but do appreciate her accommodation of minor errors.
demand to pay her payroll right away -- if her payroll was miscalculated, it needs to be corrected IMMEDIATELY.
She forced other staff to send text to me saying the business need her -- forward all records to HR.
she forced other staff to work on her schedule when I already made the time sheet for everyone -- nicely but firmly tell her that you are the direct manager here. If she steps over my toes, I have no choices but to report her conducts to HR and recommend her to be transferred.