Can you write files in a similar manner?
Yes, but you should never write to the application bundle (unless you really, really want more support mails than you care to handle). The reason for this is that applications have the same access permissions as the user that launch them. Applications are usually installed in the Applications folder, where only administrators have write access by default.
If you need to write data on MacOS X you should write to the user's Preferences folder or the Documents folder depending on what kind of file you are writing. A file like "mygame.ini" would go into the "/Users/jonasled/Library/Preferences/mygame/" folder and save files would go into "/Users/jonasled/Documents/mygame User Data/" or any location that the user selects. If write fails you should present the user with a standard dialog box to select a location.
I have a framework to do all of this, since doing it right, that is, the safe way, requires a lot of Carbon function calls. However, I'm using design patterns a lot so it might not be to the taste of most BMX coders. Further, I have not finished implementing equivalents for Win.
Jonas