3.19 The word "kosmos" (world here) links back to 3.6, where Paul lays out the rhetorical question, is God unrighteous to judge the whole world.
3.21 The word "pephanerootai" is the past tense of "phanero-oo" or to appear. Jesus has appeared (past event) but there is still a present implication (here that we are justified through faith). Also the word "testify" (martyre-oo) is in the present suggesting that the "law and prophets" still speak (L and P is used throughout the NT to describe all of the OT (Luke 24:44 is the only place that mentions the Psalms)).
3.24 The word "apolytroosis" (redemption) can mean ransom...which brings up the obvious question -- from whom to we need to be ransomed!
3.25 The word for "previously committed" is "proginomai" in the perfect tense, suggesting previous sins still had a consequence. Also, the key word here "hilasterios" is only used twice in the NT (also in Heb 9:5). It is the LXX translation of the mercy seat on the Ark where sacrifice would be made on the day of atonement. Paul seems a bit vague here in how Jesus actually functions as a sacrifice, but somehow, Jesus takes care of the demands of the law and God now offers us righteousness through faith in Jesus and his sacrifice for us.
3.27 Paul later will talk about boasting in Christ -- Romans 15.17