So far, I've visited only two places: the Bo'marr Monastery on Tatooine and the Galactic Museum.
When I visited the monastery the script with the monks was broken, and it didn't give me the Achievement medal. I read that other people have reported that later in time, I suppose it is still broken.
The Galactic Museum is currently the most interactive wonder in the galaxy, where one can explore the inside of the entities (those not open to all are one-room only), and talk to over 20 custom NPC with long conversations about specific subjects. Beware, a complete visit to the Museum with talks to the NPCs will take you hours.
The Galactic Museum gives no Achievement and I don't think it is included in the Quest plans of the admins. However, at the time of its creation I did mention that I could help writing quests specific for the GM. One of the ideas proposed during the creation of the GM was to have a quest to give an Achievement or a custom item to visitors.
As for your question on arresting, it is generally intended that wonders owned by Darkness are no-man's-land and nobody can be arrested there. Admins will intervene to sort out such occurrences and punish the transgressors. Admins have replied several times on these forums, specifically on similar questions about the Galactic Museum.
Some galactic wonders such as the Imperial or Hapan palace are supposedly not open to all, and I believe it is very easy to be arrested there. ;-)
The Holocron lists who controls the galactic wonder, and if those who have info on that could update the infobox, one could be able to know if he/she's risking his life there, or not.