You can use the search function and find threads from the last 30 design students that asked basically the same question.
Also, I hope english is not your first language. If not, then sorry for mentioning it.
Yes, an unbalanced load will cause the bicycle to lean a bit to one side. This is not a problem however, you will automatically correct for it without even thinking about it. You will lean your body the other way to compensate. The center of gravity is over the contact point of the wheels at all times (when cornering, "over" is redefined per Newton's laws).
Most people don't worry a great deal about falling, because most people do not fall very often. I've fallen once in the last 5 years, on a patch of sand. It didn't bother my panniers. If someone falls often enough to want some kind of armored carrier for their lunch box, perhaps they should take the bus.
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Work: the 8 hours that separates bike rides.