Business Visa is valid for 3 months.
Business visa can be extended if your reason is valid..Your sponsor will be applying for that if he still needed you...
Make sure that your business visa will be extended before the expiration date..
If your business visa is expired and you still here in Qatar, you will be paying QR 200 penalty day per day..
Yes, your sponsoring company can apply you a work visa, once your work visa is issued, they can apply in immigration office to transfer your visa to work visa, no need to go out to qatar..