Association of n to 1 objects in a UML class diagram?

Not in general. The arrow direction in UML corresponds to navigation possiblities. Hence, if your arrow points from the n objects to the 1 object it means that in your resulting code each of the n objects can access that 1 object.

Of course you may also want an association in which that 1 object can access the n objects, so the arrow points in the different direction. (If no arrowhead is given it means that the n objects can access the 1 object and vice versa.).

Not precisely. It depends on the type of association. If its an aggregation then the default is bi directional navigability, but you can specify the navigation to be one way.

I think that it is entirely up to the designer to decide the direction of the navigation between objects.

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