I have an American recipe that calls for Cane Sugar, is this the same as Demerara or is it Light or Dark brown sugar?
If it only says "cane sugar" without any other qualifier, just use the normal white crystal sugar you have. There is a common attitude that cane sugar is supposedly superior to beet sugar (which is the prevalent sugar in Europe), although this might well be the result of successful advertising campaigns. In any case, if you use beet sugar, I am pretty sure nobody will notice the difference.
If it says something more than just "cane sugar", (e.g. "light brown cane sugar") it could be Demerara or something else. But then your question is not answerable without describing the full term.
it depends in the recipe, if the specific aromas of molasses are important for the taste of the final product you can use a cane sugar rich in molasses (dark, brown, demerara), if not go with granulated light cane sugar, or even white sugar!
In general for all things baked I do not generally use raw sugars 'cause they're too wet, they have a very rich flavour, and their behaviour is quite unpredictable (because their exact molasses content, and therefore their water content, is unknown)