1) "What is easy for you to draw?" is probably best. "What is easy to draw?" is also good, though. As Eli said, you could answer the question with "It is easy to draw..." but there is no "it" in the question. 2) Both are correct, but "Who did you think John hired?" is better. You don't need the "that." Also - if you are talking to someone about who they currently think John hired, change "did" to "do." "Who do you think John hired?" Hope this helped.

"What is easy to draw?" is better. (We only use "it" in the non-question form ("It is easy to draw _____") because otherwise it is hard to put the emphasis on the predicate ("is easy to draw"). For the second question, neither of your options sounds acceptable, actually. If the vase was broken, the sentence should use the past tense: "Who does he think broke the vase?"