the first one I understand. The second -- is it possible for a black person with no Jewish heritage or genetics to convert according to HALACHA?
Anyone from any ethnic group can convert according to Halakhah. Technically there are some restrictions placed on certain historical groups (male Moabites and Ammonites), but since we no longer know who belongs to these groups (or even if they still exist) no one is disbarred ethnically from converting to Judaism.
Absolutely, the same as any other non-Jew who may convert. These days, almost any Orthodox community of some size has a few black converts.
http://www.beliefnet.com/Faiths/2001/02/African-American-And-Orthodox-Jewish.aspx