I want to know whether sharing or any act of benevolence by Christians should be limited to the body of Christ alone?
There are two standards for benevolence work. One concerns what the church can do and the other concerns what individuals are expected to do.
The easy one is what is commanded of individuals. Galatians 6:10 says that we are to do good to everyone (although our brothers and sisters in Christ still come first). There are other passages, but they just reinforce that Christians are expected to help whom they can.
Some people are of the opinion that the money contributed to a church continues to just be a convenient pool of the members' money and, therefore, subject to the desires of those members. Thus, as an example, they see no difference in using the church treasury to send flowers to a sick person and someone collecting a few dollars from everyone to send flowers from "the church." However, the two are not the same in the Bible.
In Acts 5, Ananias and Sapphira died because they did not make a distinction between God's money and their money. What Ananias did was sell some land and give part of it to the church. But he told Peter that they were giving the full price of the land. He wanted more credit for sacrificing than what he should have gotten. If there is no real significance in the treasury of the church, then all Ananias did was brought money and lied to the people there. Peter, however, specifically said that Ananias did not lie to the people but lied to God. The only way that Peter's statement can be true is if the money, once given, no longer belongs to the people who gave it but immediately transfers to God. If giving to the church was a man-to-man transaction, then the lie would have still been to men. However, Peter is saying once the money is given to the church, it is not a pooled resource of the members, but it is resource belonging to God. Once we realize that the money now belongs to God, the church has an obligation to spend it only on those things that conform to how God wants His treasury spent. The church no longer owns the money -- the church is just the steward of the money.
For example, let's say that the whole congregation decided to go to a national park to see wild animals and rent a bus in order to go together. As individuals, they are certainly free to spend their money in this way. It would probably be convenient for them to pool their money to rent a bus. Those going to a park are not the "church" in its religious sense, even if all getting on the bus are members of the church. If the church treasury is just a pooling of the money, then there would be no difference if the money came from the treasury or if the money came from the members all paying into a pot away from the church setting. However, if the money in the treasury is actually God's money, then the obligation would be to determine if using the church's funds to pay for the bus lines up with what God said the money could be used for.
Some people will make the argument that any instruction to the individual is acceptable practice for the church, but that would not make sense when we look at I Timothy 5:9-16 and Paul's instructions about widows. Paul said that there were specific qualifications that a poor widow had to meet before she could be put on a list to be helped by the church. Among those qualification was her status in regards to believing relatives. Believing relatives (specifically mentioned are believing women relatives) are instructed to care for their poor relative widow so that the burden would not fall to the church. This tells us that the role of the individual is different from the role of the church.
What this also sets up is a conundrum. If the church is not allowed to help certain poor believing widows, but other verses allow the church to help all the poor regardless of whether they are Christians or pagans (assuming that such a verse exists), then we have a situation where the church must help poor pagan widows but is barred from helping certain poor believing widows. Since the Scriptures don't lead to these kinds of problems, it has to be rooted in how we are looking at the verses and not with the verses themselves.
For the church to act with God's money, it has to do those things that God authorizes.
In Acts 4:34-35 it specifically says that the distribution was so that they would not have any needy "among them." Those under discussion were the church, so that passage does not extend this type of benevolence to those outside the church.
Acts 2:44-45 is similar. Those under discussion were all believers. Note that it says, "All the believers were together and had everything in common. They sold property and possessions to give to anyone who had need." It specifically says that all the believers had everything in common. To extend this pooling to those outside of the body of Christ would require the use of some other phrasing than "in common." It could be "pooled resources" or something similar. "In common" says that the collected money was used exclusively for those in the collective. Therefore, the giving to those in need would also have to be in the collective. Added to that, the whole paragraph is talking about the behavior of these new believers. Introducing poor pagans would not make sense in the overall context.
Romans 15:26-27 specifically says that the money coming from Macedonia and Achaia was for the "poor among the Lord's people." Saints are the people of God. If they are the people of God, they would do what God said. No one is arguing that Christians (as individuals) should have no compassion on the poor who aren't Christians. The context, though, is what was planned for the money that was collected by the church.
Luke 10:27-37 which is sometimes used to prove that the church can do anything the individual can do, is this time aimed at the individual. In fact, I would suggest that those who want to see church action in an individual's conduct are in some way trying to "ride the coattails" of the church. The Samaritan saw a need, and he fulfilled it. He did not go to the town and ask the town to contribute. He did not go to the synagogue to ask for money from the treasury. He did it. What I have seen is that some people like to give to God a small portion of their income and then whenever the congregation acts to help, they want to believe that they are fulfilling their obligation through the church.
That brings me to James 1:26-27. The context is the individual and verse 26 proves that the church, as an institution. is not being discussed. In fact, the context left any discussion of the church as a collective back at verse 1. Everything in the context is talking about us as individuals. Each of us has an obligation to orphans and widows. Paul said as much in I Timothy 5. If we have widowed relatives, we are to take care of them. The same would apply to orphaned relatives. We have an obligation to take them in. It is just what being a Christian is all about. To the credit of our society, we in general don't have a problem with the concept of caring for orphans. In the Roman times, it was just not so. Being an orphan (or widow) was considered a sign of the disfavor of the gods. The reasoning was that if the gods don't care about you, then neither should I. James is trying to get the Christians to see that such was not to be our attitude. Where I see a problem is when people see that James was talking to them, they brush off their personal responsibility to the "church". I've seen churches that had a $5 contribution to an "orphanage" on their list of donations and everyone in the congregation was of the opinion that such was enough to relieve them of any further responsibility to take care of orphans. God did not place the care of orphans on the church -- He placed it on our backs. Just like the case of the poor widow in I Timothy 5. There are circumstances where the church may need to support a poor widow, but never was it to be used to relieve the obligations of the individual. James is addressing the individual's responsibility and is saying nothing either positive or negative about the church's money.