Friends of mine found lots of Bärlauch on this Tour today. Must be in the small forest close to niederolm
Is it a "estágio", separate from the degree in Portugal, or something along the lines of a an Erasmus exchange? Regardless, if she has a link to the University here, either a contract or a temporary registration she might might be able to get a discount for public transportation (semester ticket or a job ticket, which costs about 35€/month). Either way, she should ask for help in her department/supervisor/colleagues. She might even be able to get a bicycle on the cheap and bike everywhere. The winter here is reasonably mild, a bit colder than Portugal, but not crazy minus temperatures, and rainy (a bit like Aveiro minus the crazy winds).
Areas to live in: I thoroughly recommend against staying outside Mainz. It will probably not be cheaper, the commute will take too long, and she might end up in a Industrial or Residential area bored out of her skull. A lot of post-grad students choose Neustadt/Alstadt (shops, pubs, bars, central), but places like Gonsenheim, Hartenberg/Munchfeld, Bretzheim, Oberstadt, are either nice areas or relatively close to Uni, sometimes in walking distance.
To check out transport connections, she can install the öffi app. This will let her test the connection available to Uni (main stop is "Universität") from any point in town. And it is in English :)