Is it possible to set up a new type of door? Not like one that opens and closes at a repetetive interval, but one like the ones in Kamino, for instance.

Yes they can be created in XSI and have will also have to be animationed there as well however you would like.
The fun bits of doors is getting the collision primitives working right.

If you are going to try and create one I suggest starting simple then progress from there that way you will know how they work.