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Drupal version: Gallery2 version: gallery.module version: Directory structure for Drupal and Gallery2
In short this would be a bad idea. There is much more to embedding Gallery2 into Drupal than just the visual aspects. For example, let's say that you allow this and then go to your standalone version of Gallery2 and delete/change a user. The embed version has no idea that you have done this and so your users are no longer synced. Another example is session handling. You need to ask yourself what you plan to gain by bypassing the embedded Gallery2. Normally it is theme or visually related. For example, you may have Drupal blocks that you do not want to display on Gallery2 pages -- this is easily done (see below). Another example is that your Gallery2 theme does not work well inside Drupal. This is more of a problem admittedly and will require work to fix it.
Simply put 'gallery/*' into the block config page in the area 'Show Block on Every Page except those listed'.
This is not currently possible to do, as Drupal expects the gallery.module to use the 'gallery' link. You can add a URL Alias (admin/build/path) in Drupal to link /photos and /gallery so that someone can navigate to http://www.example.com/gallery/photos and get to your gallery, but all the internal links will still be /gallery based and so all your albums and photos would still be in /gallery. However you can patch the module manually (http://drupal.org/node/165155) and the D6 version will contain an option to change the gallery base.
You need to disable/uninstall the Register plugin in Gallery2 (Site Admin -> Modules). Also make sure that you have removed the Login item from your Gallery2 sidebar (Site Admin -> Themes) to avoid bypass of the Drupal login.