The Visitation Actions are actions of goodwill that you can perform whilst visiting other players' cities.
Motivate is an action that boosts production to output twice the normal amount on a players' production buildings (houses and workshops). When chosen, the game will show you which buildings can be motivated by displaying a star over those particular buildings. The motivated will receive twice the normal production on that building for the current production cycle and the visitor will receive 20 coins and has the chance to receive a blueprint for a Great Building from the motivated buildings' age.
Polish is an action that increases happiness to twice the normal amount on a players' happiness building (cultural buildings and decorations). When chosen, the game will show you which buildings can be polished by displaying a star over those particular buildings. The polished will receive twice the normal happiness on that building for 12 hours and the Polisher will receive 20 coins and has the chance to receive a blueprint for a Great Building from the polished buildings' age.
You can not sabotage guild members or friends, just your neighbors.
After defeating a player in battle, you will have the opportunity to raid one of their buildings. Residential, Production, and Goods buildings can be "Sabotaged" (i.e. plundered) to steal their coins, supplies or goods. Residential and Production Buildings, which are "motivated" can't be sabotaged (i.e. plundered). Being a member of a guild can protect you from sabotage / being plundered because you get better chances to have more of your buildings motivated.
You can choose to come back and sabotage a building later, if you do not like what is currently available. Your opportunity to sabotage will expire in 24 hours.
The defeated player will see the news about their defeat. Their "News" page will present them with an opportunity to counter-attack. That button is labeled "Revenge". Revenge can have an increased probability of success (if your attacker uses the same units for attacking and defending army), because any damage from the battle will take time to heal for the initial attacker, but the defender's damage was instantly healed after the battle.
Special Event Actions
Hide Easter Eggs
During the Easter Event, Hide Easter Eggs is an action that places an Easter egg in another players' city. Easter eggs can only be hidden on decorations and only if you have Hiding Actions available. When chosen, the game will show you where you can hide an egg by displaying an egg icon over that particular decoration. The Hidee will get a chance to collect the egg the next time he/she visits their city and the Hider will receive 20 coins and the possibility of receiving a blueprint for a Great Building from the age of the decoration where the egg is hidden.