Brilliant idea, but really difficult. Even when experienced in modelling 3D objects (and using xz/xy/zy planes sometimes) the game requires still hard cognitive effort. However, cool idea and nice that you tried this out!
The mechanics are not easy to use. Showing the plane (and maybe the position) on a 3D cube in the bottom-right corner (like a "map") would really help.
Also: some of the 4D games I saw used "shadows" or other visual hints about stuff hidden nearby "behind the hidden dimension" so to say. That would help playing and would also be cool as hell! Think about it! ;-)
I had problems with the "B" (bonus?) level. I did not make it. I guess, the dimension of ZY (X hidden) is distorted or inverted or otherwise non-euclidian?
The candle was used, also usefully and meaningfully. More candle-features than lighting an area would be even cooler (but I have no good idea aside from dimming :-/ myself). Generally, a decent submission.