Welcome to the American work force. No .

To answer your poorly worded question....

yes ...

anyone can sue anyone for anything at anytime...

No. Unless there is a clear discrimination for race or gender. If she has good reviews and growing sales numbers, she might be better off finding a new job where she is appreciated.

I honestly doubt it. Unless your girlfriend has some kind of documentation from her workplace/boss that shows they have "promised" her a position higher than her current {and aren't giving it to her purposely/are giving this position to other people}, it's basically in the hands of the workplace and what they want to do. They don't have a legal obligation to give her a full time position, no matter how hard/well she works. There could be many reasons for this, namely the company's financial situation or the benefits of another worker. While there's nothing you can really do legally, you can surely be outspoken about your concerns, but delicately and professionally, not with anger, but concern.

If you're in the UK, she'd have to prove discrimination of some sort. First thing to check is if she has to put in a formal application for these jobs. It could be that she's told, "There's a job going." She thinks that it will be given to her, while her employer thinks that she'll ask for an application form. So, that's the first possibility, a misunderstanding. Before getting nasty, she should ask.

If she has definitely been following procedure correctly, she would probably have to prove some type of discrimination. She should ask for written reasons why she has been denied jobs she thinks she's been promised. Then she should look carefully at the answers and see if they reveal any hint of discrimination. It's illegal to discriminate on the grounds of sex, age, race, religion, sexuality or disability in almost all jobs. There are exceptions but they're unlikely to apply in retail where a person is already working. If she thinks that she might be the victim of some sort of discrimination, she should contact the Citizens Advice Bureau or a solicitor. Also, if she's a union member, probably USDAW, she should contact her local rep for advice.