Ok I'm no expert on matters like this either but I do design oil rigs in CAD and I think I might be able to shed some light on this for you but I might be wrong (hopefully I'm not telling you something that is wrong)
I think your missing a few things to your understandings
Ok so as far as I understand it
It works something like this
One dimensional space is simply a point in space
Two dimensional space is a line that goes left, right, (referred to as X) and up, down (referred to as Y)
Each are know as an axis but the two dimensional space that you are talking about can only be seen on a surface like a piece of paper
Three dimensional space has left, right, up, and down just like the 2d world but it also has a Z axis
This image might help
http://www.google.com/search?q=XY+and+Z+axis&hl=en&gl=us&source=android-browser-goto&source=lnms&tbm=isch&sa=X&ei=uFCjUZGDG4uE9QT3yYC4BQ&ved=0CAgQ_AUoAQ&biw=369&bih=615&sei=9VCjUdTbIYa-9QSiqoHACA#biv=i%7C6%3Bd%7CcqDasEqZDzXsvM%3A
As far as your question
is it possible that it simply exists only in two dimensional space
I'm making the assumption that you are asking this trying to understand why we can't see it
meaning does it only have length and width but no depth
and I would have to think that's not possible because wouldn't the flow of time have the same affect on all matter including dark matter
II honestly don't think there's an answer to that question at this time but it is interesting theory
however if my understanding of your question is incorrect and you're referring to the fact that it exists on another plane of existence referring to the multiverse theory then that has to do with strings and I'm not really sure that I understand how that all works
*edit*
I referred to it in the two-dimensional sense as up and down but what I really meant to say was forward and backward
up and down would in-fact be the Z-axis
I apologize for any confusion this may have caused
Also I apologize befuddled I must have been typing out my response when you posted your former post referring to your post just above this one
after reading it I see that you have a grasp on understanding dimensional space I apologize