In 1:12, Paul uses it to mean "the people in society I meet." Paul obviously didn't know every person without exception, which is what we usually think "world" means. He said he conducted himself in the world with simplicity (not mixed motives) and sincerity (not guile). He used the word "world" to mean, "the people I deal with every day."
In 4:4, Paul limits the word "world" to unbelievers -- lost people. Satan is the god of this world, that is, he's the lord of unbelievers. Satan is certainly not the god of Christians! John says that Satan cannot touch (claim) us, 1 John 5:18. So here, "world" is limited to unbelievers only.
In 5:16-21, Paul says several important facts about Christ's saving work. Paul; talks about those who are new creations in Christ (5:16-17). This is the result of Christ's reconciling work on the cross. God reconciled the world to himself -- not Himself to the world, but the world to Himself. This happened, not when we come to faith subjectively in our hearts, but when Jesus died objectively in history. God through Christ reconciled the world to Himself by not counting their sins against them. Paul preached as Christ's ambassador, that people would be reconciled to God. This is possible because God had already imputed our sins to Christ on the cross.
Here we see that "world" can't mean everyone without exception, at least not in this paragraph. All are not reconciled to God; many walk in rebellion against Him. Many have already gone to Hell, eternally unreconciled. Yet Paul says that God did in fact, in history, objectively objectively reconcile certain people to God, and so God is reconciled to them. Paul uses the word "world" (kosmos) to denote these people, but it's obvious he's referring to all those who become new creations in Christ.
God expressed love for every person by sending His son, but limits eternal life to only those who believe (John 3:16). He calls everyone without exception to be reconciled to Him. But, on another level, Christ actually bore all the sins of those who would as a result become new creations in Christ. Maybe this is why the apostles in the book of Acts never told the crowds that Christ "died for them." They emphasized the objective realities of who Christ was, and His death and resurrection, and didn't give listeners false assurance that everything was already OK between God and them.