I'll answer all your questions one by one:
Q: Can I have a map in the sidebar, like a widget, showing me the position of the actual post.
A: In the latest update of the premium version of plugin, is possible to insert the map in sidebar through widgets (the widgets are available in the menu option "Appearance / Widgets"). If you want that map displays the points associated to the post is visited, you should let empty the "category" box in the widget's settings.
Q: I want to show all points of all posts on one single map on my "browse by locations" page. Do I just have to write cat=-1 to show them all?
A: Yes, that's right, using the "cat" attribute to -1 you can display all points of website on map. The category attribute is available only in the premium version of plugin.
Q: Where do ich find the IDs of the categories? (These are the normal categories, that I use in wordpress?)
A: It is easy, go to the menu option "Posts / Categories", select the category that you want know the ID, and look in the URL on browser, the parameter, tag_ID, it is the category ID.
Q: Can I delete map points, the ones I created to do some tests? Otherwise they would appear on the cat=-1 map, right?
A: The map with cat=-1 will display all points defined in your website. If you want remove a point, in the free version of plugin, go to the page/post where the point was defined, and deletes the point's data, before press the update button of post/page.
Q: What are these template pages you are taking about? Is it for websites not made with wordpress?
A: The WordPress themes are created with template files, each of them are used depending of website section your are visiting, so, if you insert the shortcode directly in a template file, the map will be displayed each time the template file is used.