- n-ary associations are UML. But they are not so often used really. Most of associations are one-or two-directional binary ones.
- DATA diagrams are NOT UML. But the standard allows to use class diagrams for showing tables and their relationships. If you use class diagrams, it is UML, if data diagrams, it is not.
- Multiplicities are UML. You should define them as attributes of association.
- As for arrows, UML standard allows not to show them. But of course, they should be again set as attributes of association.
It seems that you use diagramming tool without UML class diagrams support. And youu need rather a modelling tool. Try VP-UML - it has free community license, including all types of UML diagrams. Or if you can install Eclipse, it has many UML plugins. The largest are EMF or Papyrus. They are free. Green UML is for starters.
I understand your troubles - many "UML" courses do not teach real UML. Many widely used tools have errors in UML realization. Some of them (IBM) are very far from the standard. The best place to check if you are on the right way, is the OMG UML 2.5 standard. It is beta2, but the content is virtually equal to the current 2.4.1, and is more easy to understand. (the current change has merely to simplify the documentation)