For how to determine the transcription factor binding sites in the whole genome, I’d use ChIP with ChIP sequencing. I’m more than 100% positive that’s the way my professor expects us to do it since he just talked about Monday.
As for the for the first question, I guess use a DNAse1 Foot-Printing Assay? A classmate of mine mentioned knockout mutations but, it’s not asking what the gene does. So I don’t see how that would be correct.