A number of events have more than one action associated with the card. Can these actions be taken in any order?
I usually play the actions in order (top down) for the most part. I think it may just depend on how the event is worded. Some will say [do X] "THEN" [do Y]. So in those cases the order does matter. Other than that you could probably do them in any order, but I don't know officially on that.
When placing a mansion off the grid it was mentioned in another post that cubes and houses could also be placed off the grid to take full advantage of all adjacent locations. Is this a correct understanding?
You are asking about placing houses and cubes next to a mansion that has been placed off the city grid, right? If so, when you place the mansion (wherever it is placed), all of the spaces orthogonally adjacent to that mansion now become part of the "city grid" as well. So yes, you can place cubes and buildings next to that mansion now.