It sounds like what you're trying to do is not so much modelling as making drawings with reusable shapes. The problem with that approach is that in UML and related modelling languages, the connectors are first-class -- they are just as important as the elements.
An EA project is a repository of elements and connectors, and a connector is no more local to a diagram than an element is; each diagram simply shows a subset of the element/connector repository. So it will be difficult to find documentation on how to achieve what you're trying to do, simply because it's not the intended use of EA.
Geert's suggestion is a good one, but in case it doesn't work for you I'll add a few words on hiding connectors.
You can switch connector visibility on and off individually in a diagram, and you can also tell EA to hide a particular connector in all other diagrams. However, when two connected elements first appear in a diagram, EA will always show the connectors until told otherwise -- 'hide in other diagrams' does not apply to future diagrams.
You could also try using diagram filters. If you give all connectors an alias equal to the name of the diagram where you want them to appear, you can then create a filter (for each) which hides connectors which do not have that alias. (Alias is better than connector name for this purpose, since the alias is not shown by default but the name is.)
Neither approach is particularly streamlined, for the reason listed above. EA is a modelling tool, not a drawing tool, and treating diagrams as individual drawings will always mean extra work.
/Uffe
