I am an asylum seeker in Italy and I want to visit my fiancee in Germany. I have a Nigerian passport and Identity card (carta di Identita), which lasts up to 11 years. I plan to visit her to ease our marriage procedure. Can I go by train to Germany with those documents?
If you are currently seeking asylum, the answer is no. You must stay in Italy and complete the procedure. At the border to Germany, the police would stop you. If they determine your identity with your biometric data, they'd send you back to Italy.
Once you have been granted asylum, you should get a Schengen residence permit and also a 1951 Convention travel document. With those you can travel, see this answer.