in korean , just like in english there is a need to describe detailed information about a subject or an object. In english we do it with a clause (whom, which, who, that + whatever information you supply in the clause). In korean it is done with a modifying structure you have pointed out. That portion in (1) means "the nickname that I could remember"--> the verb + 는 + noun. (2) comes from 없다 which is "It does not exist" with 나요 it is probably posed as an interrogation (not necessarily direct to a third person. could be a self-interrogative style)--> does it not exist? (3) 적 is similar to 때 which means "the time when"