1) In the major public debate over health care reform, President Obama sought to assure people that the government was not going to take over health care, and that they could keep their old plan if they liked it. Why did he need to do this? Why wouldn't people trust the government to make health care decisions for them?
Well, a lot of people don't trust the government anyway. I doubt they would change their minds over him making decisions for them. Also, not everyone is so "on-board" with the new healthcare plan. They don't like the concept of it, so why would they want to take part in the change.
2) Why does Obama say that insurers not paying for care “limit[s] the care you receive”? To what extent is this true? Is care paid for by insurance the only care you can receive?
I think it means that "you get what you pay for". You can't pay 100 dollars and get the plan that costs 300. You are limited to what you are paying for. If you're getting "free healthcare", you are limited to that which is free. You can't get the premium if you aren't paying for it.
3) If you buy health insurance rather than paying for health care directly, to what extent are you losing your choices in health care spending? What if the government taxes everyone and pays for health care for everyone? How does this affect your level of choice?
You are limited to what your insurance pays for. If your insurance doesn't cover it, you can't get it. (I'm not sure about how to answer the next part.)
4) Is it ever right for a President to be untruthful to get the public to accept something he sincerely believes is for their own good? If so, in what circumstances?
No, not at all. It is the President's job to talk with the people and try to improve America. I understand that he might think that this is a great idea, but it might not be. If he tells the entire truth, every last detail, then other people who would usually have no chance of getting to evaluate his plan, get to. They might see a flaw that he was ignoring because he was blinded by how "great" he thought it was. And then it can be improved or thrown out if it is needed. It could keep things from getting worse than they already are.