1. For some reason, it is necessary that the plane land in a few minutes. The speaker does not control the circumstance that is forcing the landing. Also, "must X" is somewhat formal, and so very strong -- "has to" would be weaker.

2. He is insane, but sometimes he seems sane.

3. Look: To direct one's gaze. It is possible to look toward something, but not see it.
See: To sense with one's eyes.
Watch: To look at something and see it for a period of time. You can watch something without really being interested (like TV).

4. I don't know what you mean by "rang straight". "Can/could + feeling verb" can either mean for an instant, or for a while.