Would it not be "he 'to himself' reads the newspaper"?
Does "își" inform us that the newspaper is his?
Yes, from what I've read on other replies, "își" is possessive.
Would "își citește ziarul său" be incorrect?
Someone gave a lengthy explanation on another exercise, the gist of which (if I understood correctly) was "își is possessive; do not add anything else to try to show possession bc that's nonsensical in Romanian".