1) Yes, you could sometimes see it in utility classes
class MyUtils {
public int add(int a, int b) {
return a + b;
}
}
How useful it is is another question entirely, however there's no problem in modeling it.
Another case are interfaces (sometimes represented as abstract classes), where there are no attributes (or more generally a state) allowed, only methods or method prototypes/headers.
2) Yes, this is common in anemic models, where some classes act only as data holders; as it is not a good practice to show accessor methods in the diagram, you could potentially see only attributes, and not methods; or if the attributes are public, and not needing accessors, like C++ structs.
Likewise in design models you rarely see any methods, as you are focusing on the relationship between classes, and not on their implementation behavior.