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Most parts right of the Elbe are located within the Nationalpark Sächsische Schweiz with all the rules you'd expect associated with this, but climbing is generally allowed. Left of the Elbe, the area is mostly covered by a lesser degree protection area (Landschaftsschutzgebiet), also with a well marked network of hiking trails. Some few summits are located on private property, see the guidebook. During spring and early summer, selected summits may be closed because of nesting falcons or owls - check at http://dav-felsinfo.de .
You want ethics? This is the home of ethics. Most of these are peculiar for outsiders, but have a long history. Although every few years eagerly debated, they are still valid and even legally binding by being referenced by the Nationalpark regulations. They can be summarized as:
Did you know that you can create an account to record, track and share your climbing ascents? Thousands of climbers are already doing this.
Check out what is happening in Weberschluchtstein.