This is why the linguists insist that English has two tenses: past and non-past!
These uses of what we ordinarily call “present” tense, simple or progressive, with future reference (instead of the explicitly futurive will) tend to be restricted to definite plans. They say in effect “This is what is on my schedule”.
Q: Sherry, is Bob free sometime tomorrow for a quick review?
A: Let me look at the book ... He’s in meetings til noon, and he’s out for lunch, but he can see you at three?
So sentences 1 and 2 are both acceptable, and there's no real difference between them. Discourse context will contribute to determining which you use (or whether you use will), but there's no rule you must follow.
Similarly, your final example, ‘But what do you do next year?’ I asked. ‘Yes. That is the problem,’ he replied is pretty ordinary. Questions of this sort arise, typically, when someone has described an action to be taken in the present or near future and you want to know what action will be taken in the longer term to account for the first action’s consequences. In effect, it asks “Do you have a plan for next year?”
The two questions, 3 and 4, are a bit different, because the phrase every day establishes a different sort of context for use of “present” forms. As you know, these forms are ordinarily used to describe habitual and repeated actions; every day reinforces that interpretation, and collides with a futurive reference. So these sentences are very unnatural. You might just get away with 3, Do you know what you are doing every day this summer?, if you are trying to find out if your interlocutor's calendar is fully booked. But I cannot imagine a context in which 4 would be natural; it suits better with a present referenc, something like this:
Do you know what you do every day? You leave the cap off the toothpaste every goddamn day!
Stick with the original (will live).
The main reason is that live is almost always used as an intransitive verb (without an object). Thus, we don't normally use live in the passive voice.
The only phrase (as far as I know) that live is used as a transitive verb is: to live someone's life, which is not the meaning used in your sentence.
Best Answer
For future tense, "I'll do it" or "I will do it" is the one you need.
"I'm doing it" is an example of the present progressive (or present continuous), which means that it is happening in the present. So "I'm fixing the car" means that you're doing it right now.
However, when you use the present continuous with an expression of time, e.g. tomorrow, next week, over Christmas; then it can be used to express the future. So if you include the "tomorrow" then "I'll fix the car tomorrow" and "I'm fixing the car tomorrow" are pretty much equivalent.
More info here: http://www.bbc.co.uk/worldservice/learningenglish/flatmates/episode73/languagepoint.shtml