The inviting entity at the FU Berlin is able to provide you with an invitation letter for your stay in Germany, with which you can apply for a visa. However, you will have to organize your trip yourself (booking flights, transfers, etc.). Exchange students can apply for accommodation in a dormitory at the Studierendenwerk (link). Guest academics should discuss the question of accommodation with their host at the FU Berlin. For shorter stays there is the possibility of hotel and guesthouse accommodation near the campus, longer stays require an individual solution. The liaison office will also be happy to advise you. You can find general information on the organisation and implementation of stays here.