#1. No, not really. Someone might say "I met a man, a famous writer." But I wouldn't use that in writing. In conversation, the "who is" is implied, left out. In writing, it is rather disjointed. As an introduction to a longer sentence it would be OK. "I met a man, a famous writer, who told me about..."
But not as its own sentence.
#2. Not unless "losing your keys" was an activity that you were actively engaged in. This type of structure can work in an example like "I saw a car on fire while walking the dog."
Student or Learner