- Luke says, "a demon that was mute". What does this say to you about Luke's understanding of "muteness"?
Luke understood that a demon was the source of this man's muteness, and so called it mute.
Although expressed differently, is Matthew's account saying basically the same thing? Why or why not?
This account really doesn't give the demon(s) a name.
- Are the demons identified in any other gospel accounts of evil spirits being driven out (
Mk 1:21-28,
Lk 4:31-37,
Mt 8:28-34,
Mk 5:1-20,
Lk 8:26-37,
Mt 9:32-34)? If so how?
Mark 5:1-20, Luke 8:26-37     Jesus asks the demons name - they reply my name is Legion.
Other places don't show a specific name.
In chapter 15 of the Healing book by Francis MacNutt, it indicates that "naming" the demon to cast it out can be useful.
Example: If fear is identified - "In the name of Jesus Christ, I command you, spirit of fear, to depart ....".
- Is demon possession/evil spirit always manifested by a physical illness?
No, other accounts show no physical illness. (Mk 1:21-28, Lk 4:31-37, Mt 8:28-34, Mk 5:1-20, Lk 8:26-37)
Is demon possession just an old-fashioned understanding of emotional and mental illness? Of man's fallen condition gone beserk?
In this case the man's illnes was due to demon-possession. This doesn't mean that every mute person has a demon.
We need to rely on the Holy Spirit to "discern" the root cause of someone's condition, sometimes it's demons, sometimes it's physical, sometimes it's emotional, sometimes it's sin, etc....
- How did Jesus exorcise the man's demon(s), as expressed by each of the Gospels?
Matt - Jesus healed him by driving out the demons. (v22,24)
Mark - Jesus drove out the demons. (v22)
Luke - Jesus drove out a mute demon. (v14)
None of the gospel accounts of this story say much about the manner in which the healing was accomplished. How does this compare with the details given in other accounts of driving out demons?
This does seem similar in other accounts. Casting out demons seems to be a command based on Jesus' authority rather than a prayer or petition.
- In his account, Luke warns us of a particular danger in casting out an evil spirit. What is that danger, and how can it be avoided?
If a spirit is cast out and the person is left empty, the spirit will return with others (v24-26). To avoid this the person must be continually filled with Jesus Christ.
- What do you think Jesus meant when he said, "The kingdom of God has come upon you"? Is the kingdom of God somehow present whenever someone is healed?
Yes, it is present through Jesus Christ.
Read    
Luke 9:1-2;
10:1-2,8-9.
The healing ministry is more about sharing Jesus or the Kingdom of God than physical healing. Healing goes with the message of Jesus. It is evidence that Jesus is alive today and can heal the same today just as he healed in the bible.
- In what way do the following verses cast further light on the reactions of the people? "Others tested him by asking for a sign from heaven."
People were not sure and wanted more proof.
All of the people were astonished and said, "Could this be the Son of David"?
People suspected Jesus was the Messiah.
What might we, therefore, expect people's reactions to be if we were involved in an exorcism?
This shows we should expect varying reactions.
- As short as this story is, it does give Jesus an opportunity to make an important statement about healing. What point does Jesus make, and how does this apply to you?
The healing ministry is more about sharing Jesus than physical healing. See question 6.
The other point seems to be that you have to take a stand for Jesus, you can't simply be neutral.
Luke 11:23     He who is not with me is against me, and he who does not gather with me scatters.
- In "The Brothers Karamazov", Ivan lectures his brother Alyosha about demons of rage and lawlessness as well as others. In what ways are rage, lawlessness and muteness demons?
They can keep you from seeing or doing what Jesus wants.
- What lesson(s) have you learned about healing from this account?
The healing ministry is more about sharing Jesus or the Kingdom of God than physical healing.
Luke 11:23     He who is not with me is against me, and he who does not gather with me scatters.
We need to rely on the Holy Spirit to "discern" the root cause of someone's condition.