Are the shelves thick enough to put a magnetic label to label the slot contents?

Yes - we use labeling tape that can be purchased in several different widths.

is this supposed to have a card board insert for the back or is it steel as well?

it's not steel and it's not cardboard. Think particle board

Can you hang it on the wall?

They have wall mounts for it. They're just sold separately. https://www.amazon.com/Safco-Products-9200BL-Mounting-separately/dp/B0002YXQ0A/ref=sr_1_11?ie=UTF8&qid=1499374271&sr=8-11&keywords=safco+literature+organizer+black

Safco E-Z Stor Literature Organizer, 36 Compartments, Office and Classroom Commercial Grade Steel Mailbox Mail Sorter, Heavy Duty Construction, Black

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