1) It's the object of 取り組む. It is true that 取り組み doesn't normally take を, but I think it's the only way to interpret this sentence. FYI, BCCWJ has four examples of を取り組む and 1175 examples of に取り組む.
2) Yes 仕組みづくり is what the person is hoping for, although it's not a direct object, strictly speaking. ～を期待する and ～に期待する are interchangeable.
I feel this sentence is still awkward. This person says "企業・学校・政府と", but what is the subject of 取り組む, then?
I think the sentence would be cleaner if we rephrased it like this:
I hope for a new framework which allows companies, schools and the government to work through the development of world-class human resources.