Lots of options being received for your DD OP which is great, and that you and your DD are doing the research stuff now. Re costs each country varies, I will leave to others to advise on Germany, but for those in DD's cohort who have spent last year there, it was reasonable.
If she can work out what it is she wants from her YA, that would help. I know things have changed dramatically access-wise since Brexit, but some YP don't think about this enough. This would then guide them to universities or study programmes that fit their interests, do they want a language heavy focus, experience the country culturally, are they politically minded, like arts, history etc etc. Whether it's work, teaching, language school, university etc, there is no better way, just what's right for your DD. Then some proactiveness and a little luck of the gods to throw up some good people to interact with across her year, motivating her to make the most of the experience.
If their home university does offer university exchanges, some will be more academic than others, the student may need to fulfil between 45 to 60 ECTS (which in my anecdotal experience does not fit into an au pair schedule) and modules may be competitive, or capped so there needs to be flexibility on their interests to develop an exchange programme of study. Check whether the YA forms part of the final degree classification, pass/fail or just a 'language improvement' metric.
University dependent again, classes taken will be amongst majority students who are studying that subject perhaps full time (i.e. the non language learning classes) but teaching will be in native language unless there are English only options (which does defeat the object for a MFL student) with little to no forgiveness for the student being non-native. It can be quite brutal, with some flight changes necessary this summer due to resits for some on DD's YA cohort.
I don't know how academic your DD is, but if she is, the university option is an excellent one. German is and has been on the decline for a while now in UK, so some will have good scholarships and awards for increasing uptake so do look out for these in researching as they can help on supplementing funding.
Good luck!