I'm a Canadian student living in New York and a company will sponsor me. How much will it cost the company?

Students are forbidden to work. You will lose your student visa. Furthermore, you do not have the necessary qualifications to be eligible for any category of employment visa. You must have a degree and a minimum of 2 years experience in your field beyond your degree to be eligible for the most popular type of employment visa, the H1-b. The company cannot get you a visa.

As a student of a F1 visa, you will not be able to work unless you have a work authorization (and that is generally limited to on campus or study related) from CIS.

You can not be a F1 and a H1 at the same time.

If you need the work to pay for the school, you are already out of status, as to get the F1 and valid SEVIS paperwork, you and the school had to certify that you paid for the schooling and have the necessary funds to provide for your support while in the United States.

Yes