yes it does, but you have to make sure you select save as package, then everything will be included in the file. so when you use in another program, you can always find any elements of your document in that package folder. doing this, you can also take your file to other computers this way.
InDesign CS3 runs on Windows (XP SP2 or later) and Mac OS X (10. 4. 8 or later, G4/G5/Intel processor). However, it does not currently run in Wine under Linux.
Yes,I have not used it personally,but the computer apps class in my school uses it in both the pc lab (dells running XP Pro) and the mac lab (eMac G4's),and they have never had any problems opening work from the other lab on any of the computers in the building.
The CS3 version of Adobe InDesign is available for both Windows and Mac (PowerPC and Intel-based) although different product media is required for different platforms.