Can anyone clarify difference between archive-{posttype}.php, type-{posttype} and date.php?

You should consider asking one question at a time.

And lastly: is there a template to be
created which outputs all the years
and months of the custom post type
with wp_get_archives()? Or do I have
to create a different template to
create them for each post-type?

You mean like this: http://scribu.net/wordpress/smart-archives-reloaded