Yes, you are allowed to marry. Your legal status doesn't really matter in this regard, even though it might have some implications that you need to keep in mind. For example, it might be a problem to hand in your passport because if your asylum procedure ends with a negative result you can get deported. That won't happen if you were a fully recognized refugee.
In order to marry in Germany you and your fiancé need to get in contact with registry office (Standesamt). You have to provide a number of documents (passport, certificate of birth, certificate of no impedimend and maybe some others too). Foreign documents need to get translated and (sometimes) also verified. You can then arrange a wedding date with Standesamt.