I can't remember any issues with gmail. I just entered my address and password into the Mail app, and now gmail appears as well as my hotmail.
Yes, it is optional. If you are using it in association with an application (like an email client) you must go to a website and get an application specific password as the OP pointed out. Otherwise it will not work.If my mind serves me correctly the 2 step authentication should be optional for added security.