Tempaltes are simply PROGRAMMING aids that help at compile time, not run time. Templates allow you to code things only once and then compile them over a whole host of particular instances, but they DO NOT provide any special RUN TIME behaviors. Each instantiation of a template using different parameters is a whole different class to the compiler, and at run time. The template keyword just allows the PROGRAMMER to avoid duplication, it does NOT save any code space over writing seperate classes for each of your uses.
Also note that the features provided by polymorphism are a superset of the features templates provide, so if templates don't suit your needs, consider writing the class to manipulate a specific defined interface (preferably a class whose members are ALL virtual, pure or otherwise). Ex, an ObjectList, which is list class which works on classes of type Object, which is the base class for your other types. Please realize I am not advocating only one of these solutions over the other...in fact my current project utilizes both for different circumstances.
BTW - the new standard keyword "export" attempts to allow templated classes to be managed more like other classes.
Template definitions must be availible to the code that wants to instantiate them for the same reason that a class declaration must completed before instantiation: The compiler needs enough information to generate code. It's really easy to understand if you think of the template similar to an inline function or a macro.