Can a professor ask for money directly from students to print out handouts for class?
A professor should not be asking directly for money from the students. If the professor is scanning and printing things out for the students at her own expense, then something is wrong. Either the assignments and handouts should have been compiled into a course book, or the department should be helping to defray the professor's expenses.

Regardless of the request, I would be very uncomfortable giving money directly to the faculty member.  It could be paid to the department, which would then reimburse the faculty member. But I would never hand cash or a check over to the faculty. This sets a very bad precedent.