W2 part time employee working on own schedule

Hi. I am currently working as a 1099 employee, since I was on a probation period. The employer offered to convert it to a a part-time W2 position with health insurance, there is not enough work for full time, which is good because I can look for another part time position. I work remotely from home. I am not sure if its more beneficial for me to work as a contractor, a business or as a part-time W2 employee.

Is it possible to work on own schedule or being paid a flat weekly rate on W2?

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