The need of such collection is because the gospel apparently reached a large number of widows in Jerusalem who were mostly poor (Ac 6:1-6) and poverty was aggravated by the failure of crops during famine (Ac 11:27-30).
Elsewhere Paul describes this collection in terms of:
There is some significance to their setting money aside on the first day of the week rather than "once a week", probably the beginning of a weekly gathering for the breaking of bread.
Paul encourages a consistent and purposeful approach to ensure a greater gift than a single collection at the time of his arrival. According to 2Co 8:10-11 they had made a good beginning but had failed to follow through with it.
Paul is eager to spend considerable time among them, to solve the breakdown in relationships between him and them.
"Help me on my journey" means providing a person with food, money, and travelling companions. It sounds like a peace offering on this matter. Although he has refused to take money while with them (ch.9), he now offers them the opportunity to assist him on his further journeys, so that in this way they, too, can have a share in his ministry.
The two facts of "a great door for effective work has opened to me" and "there are many who oppose me" are descriptions of Paul's lifelong labours as a Christian missionary.
The opposition was because the success of Paul's mission Ephesus finally brought about the conflict with the hawkers of souvenirs at the temple of Artemis (Ac 19:23-41).
In 4:17, Paul explicitly said that he had sent Timothy who worked with Paul in the founding of this church. Paul knew that the sentiment against himself was strong indeed and that it may overflow toward Timothy. Paul warns them that no one should treat Timothy with contempt.
According to 2Co 1:15-2:4, shortly after this letter Paul pays a sudden, unexpected visit to Corinth. Perhaps the return of Timothy gave him reason for even greater alarm with regard to the Corinthian church. However, this brief visit developed into a major crisis in Paul's relationship with this church, which took at least two more letters and two visits from Titus, a person of extraordinary grace, to straighten out (2Co 2:13; 7:6-7).
It is a response to their letter (as indicated by the familiar "now about"), possibly a request for Apollos' return. Paul asked Apollos to return but Apollos resists the imploring. Apollos' reason was probably his desire to not involved in the internal strife being carried on in the church in their names. This speaks much about the true Christian character of Apollos as well as Paul.
Paul's exhortations: (a) on guard: watchfulness in light of the Lord's return, watchfulness with regard to the devil (1Pe 5:8) or to corrosive influences (Ac 20:30-31); (b) standing firm "in the faith": both the content of faith and the act of trusting; (c) be people of courage and be strong: remain steadfast courageously in the face of doctrinal errors and behavioral aberrations
"All things done in love" would include: (a) the quarrels in the name of leaders in ch.1-3, (b) their attitude toward Paul in ch.4 and 9, (c) the lawsuits in 6:1-11, (d) husband-wife relationships in ch.7, (e) the abuse of the weak by those with "knowledge" in 8:1-10:22, (f) the abuse of the poor at the Lord's Supper in 11:17-34, (g) the failure to edify the church in worship in ch.12-14. This reminds us of the saying: "In all, charity."
Stephanas is loyal to Paul in the present tensions within the community. Paul mentions his household as qualified for leaders in: (a) they were the first converts (not a new convert, 1Ti 3:6), (b) they devoted themselves unto service for the saints (ministering others, not someone who sits back and makes decisions).
Submission to leaders means submission in the sense of voluntary yielding in love (1Th 5:12-13, Heb 13:17). The emphasis is not on the action of submission rather than an attitude of submission which is even more difficult.
Being visited by longtime friends in faith is a season of refreshing in the Lord, both because of the renewal of personal friendship and also exchange of news of other believers.