5 could be right in certain context. It makes it sound as if the person might not have a car. Which if the speaker is unsure if the person has a car or not, it would be correct. If the speaker knows that Mike has a car, but the car may need to be replaced, it might be something like "I wonder if Mike needs a new car." It just really depends on what you meant for that sentence. Number 9 is also correct in certain situations. For example if you were showing the item that is necessary for his work. But it makes it sound as if the work is not finished yet. If that is the case that is fine, if not you should replace is with was. Which would mean that the work is finished. For some reason the word that in the first three sentences sounds odd to me. I am not sure if it is incorrect or not and I am unsure why it sounds odd. Maybe it is just me.