I think there's an implied meaning in using "will" vs. "would" in hypotheticals. In your first example, would and will are both correct. Will, I believe implies a higher level of expected certainty.
By that I mean, if you ask "what will happen" you're expecting the reader to infer that the answerer knows what will happen. If you ask, "what would happen" then the reader will likely infer that the answerer is making an educated guess as to what the result will be.
The following 3 sentences don't appear to be asking what you intend to ask.
The second example means, "what will happen if I am the kind of person who would actually say to my boss that I'm not coming into work tomorrow?"
The third means, "what will happen if I will say to my boss . . .?" This is a great example of how will and would have different probability assertions. The answer to this question is "you will say to your boss that you will not come tomorrow."
The fourth is just like the second except that there's an implied speculation.
Revision: After working through some of your questions in the comments, I believe I realize the problem you're having.
It appears you're looking at the future condition and expecting to put the verb in the future tense. Id est, "I will say." I believe these are called conditional sentences, specifically future conditional sentences.
There are two general forms in English:
If/When - Future Condition - Simple Present Result
If/When - Simple Present Condition - Future Result
So, your question is technically, "If I say to my boss today that I'm not coming in tomorrow, what will happen?" In English, we can arrange this question to be, "What will happen tomorrow if I say to my boss today that I'm not coming in?"
If you were to ask, "what will happen if I will say to my boss that I'm not coming to work," you could rearrange that to be "If I will say to my boss that I'm not coming to work, what will happen." I think that's how other posters have read it (and that's how I read it) and that's why it sounds confusing.
http://en.wikipedia.org/wiki/Conditional_sentence
http://www.englishpage.com/conditional/futureconditional.html
Or, Google "Future Real Conditionals."
Best Answer
Yes, I agree. The first option is the best. 'Beginning' in the second option is superfluous because it means pretty much the same as 'start' and 'from' in the third option is superfluous too (if the starting point is tomorrow, 'from' is already implied).
If you chose to say "I will look into it tomorrow" instead, this would still be correct, but your sentence would have a slightly different meaning. The first - "I will start ..." implies that it will take you more than one day to complete the task of looking into it, whereas the second "I will look ..." implies that you can complete the looking into in one day.