I find it striking that Paul spends so much time at the end of his letters sending greetings to the church from himself and his associates.  Who are these people that Paul mentions in Colossians 4?

Tychicus was from "Asia" and accompanied Paul at various points in his ministry unto the very end of the apostle's life. He is here called "a beloved brother and faithful minister and fellow servant in the Lord" (cf. Acts 20:4; Eph 6:21; Col 4:7; 2  Tim 4:12; Titus 3:12.Onesimus was a runaway slave of Philemon's, an influential Christian at Colossae, and he was converted under Paul's ministry and so became "useful" (the meaning of his name in Gk.) as a brother in the Lord  (cf. Col 4:9; Phlm 1:10). Aristarchus was one of Paul's travel companions (Acts 19:29; 20:4; 27:2; Phlm 1:24) and is now a fellow prisoner for the cause of Christ (Col 4:10). Mark (also called "John Mark") has quite an interesting story with Paul.  He joined him in ministry but then abruptly left and went back to Jerusalem, and Barnabas and Paul actually parted ways over what to do about Mark (Acts 13:5, 13; 15:37, 39). Peter calls Mark "my son" in 1  Pet 5:13, and according to church tradition Mark was converted under Peter's ministry and ended up writing the Gospel of Mark. Evidently Mark and Paul were reconciled, for in 2 Tim 4:11 Paul writes that Mark "is very useful to me for ministry" and in Col 4 he tells the church to welcome him. Some of Paul's associates like Jesus who is called Justus and Nympha are mentioned only here in the NT. Others are well-known, like Luke "the beloved physician,"  a co-worker of Paul's until the very end of his life (Col 4:14; 2  Tim 4:11; Phlm 1:24) who according to church tradition wrote the Gospel of Luke and Acts. While Luke was faithful to the end, Demas evidently was not (Col 4:14; 2  Tim 4:10; Phlm 1:24). Epaphras is a native of Colossae and seems to be Paul's connection with the church there.  He is a faithful, servant-hearted prayer-warrior on their behalf (Col 1:7; 4:12; Phlm 1:23). Paul is nearly finished with the letter but takes a moment to directly address one individual- Archippus, saying "See that you fulfill the ministry that you have received in the Lord" (Col 4:17; cf. Phlm 1:2). Perhaps this "fellow soldier" was discouraged or wavering in some way in ministry, and Paul gives him a direct, pastoral word of encouragement.

Why does Paul end the letter the way he does in v. 18? “I, Paul, (1) write this greeting with my own hand. (2) Remember my chains. (3) Grace be with you.”

(1) Paul mentions his imprisonment earlier in the chapter when he asks the church “At the same time, pray also for us, that God may open to us a door for the word, to declare the mystery of Christ, on account of which I am in prison—” (Col 4:3). Being in prison in the ancient world carried with it an incredible stigma and deep shame, and Paul is calling the church at Colossae to remember his chains, to not shy away from the suffering that the gospel of Jesus sometimes brings (cf. 2  Tim 1:8, 16).

(2) Paul’s regular custom was probably to dictate his letters to a secretary, which is clearly indicated in Romans 16:22.  Even though he often dictated his letters, Paul draws attention in several places to writing a greeting “with his own hand”:
“I, Paul, write this greeting with my own hand. This is the sign of genuineness in every letter of mine; it is the way I write” (2  Thess 3:17; cf. 1  Cor 16:21;Gal 6:11; Phlm 1:19). Paul wants to let the church know that this letter really is from him, that they can have confidence of its truth and authority.

(3) Paul begins his letter “Grace to you and peace from God our Father” (Col 1:2), and now he ends his letter by drawing attention to that same grace: “Grace be with you” (Col 4:18). John Piper says, “Paul has in mind that the letter itself is a channel of God’s grace to the readers.” The implication for us is that “grace is ready to flow to us every time we take up the inspired Scriptures to read them. And we learn that grace will abide with us when we lay the Bible down and go about our daily living.”