Hello! I think I can help you with these. I apologize if I say something that is confusing, and feel free to ask questions.
Numbers 1 (He works at/in/for/with IBM.) and 2 (He works at/in/for/with McDonald's.) are very close to each other in meaning, so I will try to answer both of these at once.
The generally correct answer for this would be "He works for IBM." I understand your trouble with these. Most people would say "for" because it tells the reader that IBM is the employer, and "he" was the employee.
With in, it says to the reader that "he" works physically inside IBM, which is probably not what you want for it to mean and is phrased difficultly (or, in short, you just don't say it!). For example, you would say that I worked in the kitchen, but not that you worked in the specific resturant (such as McDonalds)
With at, it too says to the reader that he works physically inside IBM, but, well, it's correct. It uses IBM as a place rather than an employer, and it is assumed by the reader that by IBM you mean the buildings at which you would work at IBM.
With, well, with, it says to the reader that you and IBM of are equal value/worth, while you presumably mean that IBM is more important than you, and you are an employee.
To tell you the truth, the only one of these that you really couldn't say would be "in," and slightly "with." With the others, though meaning slightly different things, in the type of conversation you are talking about, all will work. The English language is surprisingly flexible like that.
3. He is with IBM/McDonald's.
This is an oddly put sentence. Either IBM or McDonald's would work, though you may want to use a word other than "with" for the reasons above.
4. He works for/under me.
While both would work, one would generally say "for," as, in this example, the "under" could be confusing to the reader, as they could think that you mean that he works in the floor "under" you, and, other than that, the term "under" in this context is generally no longer used.
Once again, feel free to ask questions.
Student or Learner