You can select all of the objects and then go file -> Export and that’ll churn it out as an FBX that you can then re-import and it’ll be it’s own little model.
The only problem is that with it being made from reshaped cubes the UV wrapping on it may screw up which will then cause textures applied to it to become warped and distorted.
You could probably re-do the unwrap in a separate program such as 3DS .
Regarding making it go up and down, that’ll be a matter of creating a blueprint out of the model which has a timeline which controls how high it can go up.