The Visa and/or permits you will need while you are in the Netherlands (and how much they will cost) will depend on your own nationality. In most cases you will make your application through HU rather than directly.
Read more and follow the procedures on the HU website here: Visa Procedures. However, if you would like to do some more research in the meantime you can also have a look at the information here: Study in Holland website.
HU does not own any student housing but has an agreement with the housing provider SSH Short Stay. Places there are limited but there are a number that are reserved for students coming to HU on exchange.
Reading about WORLDREP in 2015, I was immediately onboard with the program. I had always known that I would do what I could to go out as an exchange student. I remember my very first day at the Danish School of Media and Journalism. We, the new students, were told to come up with questions about the school and figure out who to talk to in order to get answers. The only question on my mind was ‘How can I get out of here?’. On exchange, I meant of course.