rabbitFoot on "Plugin install Page Templates"

I am writing a few plugins which require Page Templates;

1) Do these have to be installed in the current theme (and others if changed) or is there a shared place I can put them? If require to be installed in each theme then what is the standard / recommended method?

2) Is it best to use the plugin to create and write the files out or is there an inbuilt method for placing the templates?