Answer to Question 1
musical ethnography.
A topic is a subject viewed from a particular angle, from a certain perspective, and with a limited goal in mind. It enables your analysis and interpretation of the subject.
The Jewish Cantor is a subject; Musical training of Jewish cantors in New York City is a topic (The cantor is viewed from a special perspective: education.).
Answer to Question 2
As a participant you actually perform in the musical situation you are studying; you will have the benefit of learning about the music you are studying from the inside, but as a participant you can lose your ability to have an objective overview.
As an observer you forgo any participation and simply observe (and perhaps record) the music you are studying. This can save time, but your presence as an observer can be distracting and alter the musical situation you are trying to understand.