You've pretty much exhausted your options already. The only other way is if an employer can get a permit for her on the basis that she would be much better than any Swiss/EU candidates he could find and that sounds unlikely to me. https://www.bfm.admin.ch/bfm/en/home...zulassung.html
No, she is not allowed to live with you unless you agree to be financially responsible for her for 5 years, even if the relationship breaks up and she stays in Switzerland afterwards. If you willing to do that then you could apply for a concubine permit for her, BUT it's unlikely it would be granted for anything other than a long term, committed relationship - not one for people who have only met on holiday. If she wants to come here and study then she has to show she can support herself, not you do it for her.
My suggestion: just keep visiting back and forth between countries, that's all you can realistically do. If the relationship is strong enough it'll survive a bit of long distance romancing. But frankly to me it sounds more like she's looking for someone to pay her way into Europe. Au pair rules are the same for the EU as Switzerland, i.e. age limit is 25, so if she really wanted to do that she would have done it already. Same with studying, if she really wanted to do it she'd have been saving up to afford it herself.
Studying in Germany may be possible as tuition is free there, but again it depends on whether she can support herself financially, what course she wants to do (not all are taught in English so she may need to speak German) and whether she's really serious about it in the first place. http://www.studying-in-germany.org/ http://www.topuniversities.com/stude...-study-germany