Does swedish snus cause damage to the stomach?

Possibly. A study of almost 10, 000 swedish men in the international journal of cancer (2008) didn't statistically confirm an increase in combined oral and pharyngeal cancer.Other comments in renowned journals such as the british medical journal and the lancet suggest a probable increased risk of pancreatic cancer as a result of snus use.
Almost certainly. Snus, like any other tobacco product, can cause cancer. Cancer's of the mouth and throat are most common but cancer of the digestive tract (stomach, pancreas) and possibly even the lung are also possible. If you think about it, cancer is pretty extreme, so even before it would cause such devastation, it is going to be causing other, less severe troubles.