Interesting that you are looking at the research questions surrounding missionaries and miracles/healings. Perhaps you are considering being a missionary yourself? Anyway, I will try to answer your questions. "how common is it that Christian missionaries come back from their mission trips reporting extraordinary anecdotes?" This is a good question but I think it is more complicated than just a certain relationship between missionaries and miracles. In other words, what makes a missionary successful in performing signs and wonders? The bible has several factors to consider. First, If the missionary is baptized with the Holy Spirit.
Acts 1:8 (KJV) 8 But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.,"
Along with the baptism of the Holy Spirit, (often accompanied with speaking in tongues) there are other gifts and anointings to consider. Gifts of the spirit, (I Cor 12), ministry callings (Eph 4:11), Offices and gifts (Rom 12).
Of course it is God giving all these gifts and callings, that no one should boast. Much too is up to the individual. how much do they pray, fast, how well are they taught? How much love and other fruit of the spirit do they show? How much are they led of the Holy Spirit?
In addition to these missionary qualities, signs and wonders may also be dependent on the hearers. This seems evident by
Mark 6:5-6 (KJV) 5 And he (Jesus) could there do no mighty work, save that he laid his hands upon a few sick folk, and healed them. 6 And he marvelled because of their unbelief. And he went round about the villages, teaching.
Others also think it is somewhat based upon how desperate the people are. If there is no access to a doctor, then with the stakes higher, life or death could depend on a single meeting. The last two reasons might be why we often hear far more about healings/miracles in Africa versus a country like Australia. Could be the same missionary but different results based on the place they are ministering.
Of course the best thing is to go wherever God would lead and leave the miracles and healings up to him. Concentrating on miracles and healings alone would be short-sighted when the goal is getting people born again and discipled in Christ.
To sum this up, I think that missionaries that are called and gifted should have some success (through Christ) and be able to share stories of miracles, healings, supernatural access to places and people that were unexpected, encounters that were purely orchestrated by God, prophecies that change lives etc. I would not just limit God to miracles and healings. Not all will have the same success, nor should we measure their success by the size of their crowds or the number of healings, etc.. The main thing is just to be faithful to do what God leads us to do.
To study this further, I would look for books like Hagin's "understanding the annointing." or others that address how to be more effective. Some of the things like prayer and fasting can begin right where we are. Hope this helps, God bless.
