Check out this YouTube page:
She is in Australia and gives a 5 or 6 step tutorial on how to make a topsy turvy cake. That should help a lot! I'm going to attempt my first one in a few weeks.
The box is probably not a cake topper, but you could certainly use an ornament that looks similar if you don't wan to make one. If you did want to make one, I would try either making a square cake and covering in fondant or making a sugar paste box. Just make all the sections separate (make them thicker than you would for flowers), then put together with some melted white chocolate or royal icing.
You should be able to travel with it for an hour as long as you dowel the whole thing from top to bottom and make your dowel go through to the bottom of the cake drum. If you're unsure, just assemble it when you get there. :)
You can freeze it, but you need to make sure you don't touch the layers as they come back to room temperature because they will have condensation on them. You need to wait until that goes away before you pick up the layers.
The lollipops look like they are just fondant twisted together and swirled around. Then you can push that on a lollipop stick and put aside to dry.