Only during the summer if she/he intends to enroll in the following Fall Semester. Otherwise you will need to change the title to a non-student title.
Work study programs allow 20 hours per week. Institutional student employees can work as many hours as the department wants. Any hours worked on campus over 40 in a week is subject to overtime.
Most commonly, the increase in tax deductions is due to having social security and medicare (FICA) taxes deducted. You must be enrolled at least one half time each semester to qualify for the student FICA exemption. If enrollment drops below one half time, you no longer qualify for the exemption and these taxes will be deducted from your pay check.