As for your first question: When Jesus says something happened in the history of His people, Israel, you can rest assured it happened. He is the Alpha and the Omega, the first and the last, the one who knows the end from the beginning and the beginning from the end. Nothing in history escapes His notice.
As for your second question: The lepers who resided in Israel during the prophet Elisha's ministry evidently did not have the faith of Naaman the Syrian, a lone Gentile Captain of the Syrian army who had heard of Elisha's miraculous powers through a Hebrew servant girl who had been taken captive in a battle between Syria and Israel.
As for question number three: Of course Naaman was healed. Again, if Jesus said he was, then he was. As Inspector Clouseau in the Pink Panther film would say, "Case is sol-ved."
Let's contextualize Jesus' comments to the members of the synagogue who heard them.
First, we know that Jesus was not able to perform many miracles in his hometown of Nazareth. Mark tells us
"And [Jesus] could do no miracle there except that He laid His hands on a few sick people and healed them. And He wondered at their unbelief" (6:5,6).
When Jesus finished his remarks about a prophet's not being without honor except in his hometown and among his own relatives, and then launched into a little history lesson that took his audience back to the days of Elijah and Elisha, He knew His words would "hit home," which indeed they did! After hearing Jesus mention two Gentiles who were recipients of miracles in the days of the prophets, we read
"And all the people in the synagogue were filled with rage as they heard these things" (v.28).
They would have cast Jesus off a cliff and then rained down stones upon His body until He was dead, had He let them. It was not "his time," however, and He simply "passed through their midst" (v.30).
As Constable observed in his notes contained in the NET Bible,
"Jesus did not say that Elijah and Elisha went to Gentiles because the Jews rejected them but because God sent them there. God sent them there even though there were many needy people in Israel. Nevertheless Israel then was in an apostate condition. The three and one-half years was a period of divine judgment on Israel (cf. Dan. 7:25; 12:7; Rev. 11:2-3; 12:6, 14; 13:5). The implication of these two illustrations [of the Zarephath widow and the Syrian captain] was that God had sent Jesus to Gentiles as well as to Jews. The Nazarenes, therefore, should not expect preferential treatment. Jesus ministered to Jews first, but He also ministered to Gentiles. These examples would have encouraged Luke’s original Gentile readers since they had a similar mission."
Jesus' and His disciples' primary audience, then, comprised Jewish people in the main, but they by and large rejected Jesus and His message of repentance.
In perhaps Jesus' most scathing denunciation of all, He told the crowds of people who gathered around Him after He had sent the Twelve on a preaching mission, people who were from the Galilean cities that failed to repent even though He had performed many miracles there:
"'Woe to you, Chorazin! Woe to you, Bethsaida! For if the miracles had occurred in Tyre and Sidon which occurred in you, they would have repented long ago . . .. Nevertheless I say to you, it will be more tolerable for Tyre and Sidon in the day of judgment than for you. And you, Capernaum . . . if the miracles had occurred in Sodom which occurred in you, it would have remained to this day. . . . It will be more tolerable for the land of Sodom in the day of judgment than for you'" (Matthew 11:20-24).
We're all familiar with Paul's statement about the gospel being the power of God unto salvation to everyone who believes, to the Jew first and also to the Greek (Romans 1:16). We're also familiar with Jesus' interaction with the Syrophoenician woman--whom Mark calls "a Gentile of the Syrophoenician race"--in which Jesus engages in a little playful repartee with her:
". . . she kept asking [Jesus] to cast the demon out of her daughter. And He was saying to her, 'Let the children be satisfied first, for it is not good [proper] to take the children's bread and throw it to the dogs.' But she answered and said to Him, 'Yes, Lord, but even the dogs under the table feed on the children's crumbs.' And He said to her, 'Because of this answer [word] go; the demon has gone out of your daughter.' And going back to her home, she found the child lying [thrown] on the bed, the demon having left" (Mark 7:26-30).
While Jesus' primary ministry was to "the lost sheep of the house of Israel" (Matthew 10:6), He nevertheless rewarded faith wherever He encountered it,
whether it was at a well in "Samaritan country" where a woman with a shady past experienced Jesus' forgiveness when she believed He was the Messiah (John 4:7-30, 39-42);
whether it was in Tyre where a Syrophoenician woman who--not so coincidentally came from the same general vicinity of Captain Naaman, the leper of 2 Kings 5--begged for the life of a daughter being ravaged by an evil spirit;
or whether it was in the big city where a Roman centurion's servant in dire distress received a healing long-distance when his master, in faith, asked Jesus to heal him.
Each person approached Jesus in faith, and Jesus, who was not a respecter of persons, gave each of them their healing.
What was Jesus' reaction to the centurion's faith?
- "Now when Jesus heard [the centurion's request], He marveled and said to those who were following, 'Truly I say to you, I have not found such great faith with anyone in Israel'" (Matthew 8:10).
At this point, the unbelieving Jews who witnessed the miracle were probably feeling a bit salty, having heard Jesus' clear rebuke of His "own people" (see John 1:11), whom He considered to be lacking in faith. In effect, Jesus was saying, "Shame on you; you should know better!"
Second, the notion of jealousy--or the "jealousy factor"--is relevant in Jesus' approach to His own people vis a vis outsiders to the faith. Paul speaks of this in Romans 11, where he says,
". . . By [Israel's] transgression salvation has come to the Gentiles to make [Israel] jealous. Now if their transgression is riches for the world and their failure is riches for the Gentiles, how much more will their fulfillment be! But I am speaking to you who are Gentiles. Inasmuch then as I am an apostle of Gentiles, I magnify my ministry, if somehow I might move to jealousy my fellow countrymen and save some of them" (vv.11-14).
In conclusion, while on earth, Jesus looked for childlike faith, He looked for sincere belief. Whenever and wherever faith and belief were evident, Jesus saved, healed, and forgave. Ultimately, the Jews rejected Jesus as their Messiah and King. Consequently, in the years after His resurrection, Jesus' message was taken to more and more Gentiles. One day, however, the "fullness of the Gentiles" will signal the end of the "church age" (see Romans 11:25), and God will once again turn His attention to His people according to the flesh,
"and so all Israel will be saved; just as it is written, 'The Deliverer will come from Zion, He will remove ungodliness from Jacob.' 'This is my covenant with them, When I take away their sins'" (vv.26,27).