Changing visa

Hello,

I got a job offer while studying in my japanese language school and they will sponsor my visa. My question is can I quit school as they need me asap?

My visa will expire in 2019 but is a student visa and I need to change to a working visa. When I go to the Immigration Office can I still stay here and work while the process is being made?

And my third question is, my company told me they will do everything but at the end I will need to go to the Immigration Office right?

What you want is a change of status, and it is amply documented here and elsewhere if you care to do a search.

As mentioned, you (or your employer-to-be on your behalf) will be applying for "a change of resident status."
Once you get the application submitted, you can stay in Japan while it is being processed, but you cannot start your new (full time I assume) work until you have the new status granted.

during the processing, you are still in student status. if you quit the school during the processing, you can't work even in part-time (28 hrs per week). (to work in part-time, you have to be a student.)
after the application is granted, you are in working status. you can work in full time.