Anger is part of the process, too, though please don't let your mum know you are angry for her not bringing this forward sooner. Being angry isn't going to change the past or the outcome. So far, despite the delay, you are having all the news break your way - its a relatively small tumor, probably estrogen driven (don't think you mentioned if it was?), no obvious nodal involvement. If she is having surgery first then that is also a good sign - a larger, more aggressive, or different hormone type of cancer would have chemo first.
As others have noted, breast cancer is highly variable depending on a lot of different inputs - this is not one-size-fits all and treatments have started to reflect that. Until you have walked this path, though, you wouldn't know. Over the next few weeks you should learn and be used to the terminology and your fear and anger will subside.
Also, just to note, the Stages referenced by @SudokuWillNotSaveYou are not that quite cut and dried. Staging is done by tumor size (T), node involvement (N), and distant metastases (M) as well as hormone receptor type and grade. Stage III typically means a high number of nodes as well as some local spread to nodes in the collarbone. Stage IV is spread to anywhere else including most typical sites of bones, liver, lung, brain. Breast cancer at all stages is treatable, but it is not curable at Stage IV.