The third part is the question of whether being a professional (full-time) is a necessary characteristic of a missionary.
In other words, can one be a volunteer, be a part-time missionary, be a short-term missionary, a tent-maker, however one wants to say that one is not a full-time professional… can they be called a missionary?
The classic missionaries of the New Testament were wanderers. Paul, Barnabbas, Apollos, Philip, and more (including Christ) travelled from place to place. Some worked to fund themselves. Some did not appear that set roots long enough to fit the role that some would consider as long-term missionary (at least within a regional culture).
While I understand why one might consider short-term missionaries as not “real missionaries”. That being said… I still have problems with narrowing the term. Certainly, being “professional” or paid makes no sense as defining a missionary.