Spoiler-Filled Thoughts
1. Captain America-- I don't think he grew old in the current timeline. The film specifically laid out the impossibility of that. He went back to 1945 and lived out his life. When the time came he traveled back to the original timeline (let's call it the OT) to hand over the shield and, presumably, to live out his remaining life.
2. The above opens up an interesting possibility. One assumes that Cap's new timeline went very differently. He didn't just marry Peggy and retire. He no doubt rescued Bucky in '45, took steps to prevent Thanos from winning in that timeline, etc. Maybe he even found a way to keep the Dodgers in Brooklyn. However, that means that there is still a frozen Captain America in that timeline that those in the OT could go get and bring back so they still have a young, healthy Cap. They won't do that, but it's "a thing."
3. If I understand it correctly, when Hulk borrows the time stone from the Ancient One, he creates a divergent timeline. He returns to the O.T. with the stone, stuff happens, then Cap has to return the stone. Their time travel device has to do more than travel in time. It has to allow him to select among likely infinite timelines, because if he went back to that moment in his own timeline, the Ancient One would still have the Time Stone. So Cap journeys to numerous points in time, on numerous timelines.
4. If 3 is accurate, does the OT still have to worry about Thanos? There are infinite Thanoses on infinite timelines. Could one of them collect all six stones and somehow learn about his defeat in the OT? Or perhaps more broadly, realize that he may have been defeated in some timelines, and go to the OT to finish the job? It seems the OT is the only 1 of the 14,000,605 timelines Dr. Strange viewed where Thanos failed, but it stands to reason with infinite timelines there may be infinite defeats of Thanos, which is a lot of traveling for someone who just wants to farm, so maybe this isn't an issue?
5. Where does Cap return the Soul Stone? Does he get a reverse prize from the Red Skull? Maybe that's how he ended up in 1945? He is the first person to bring back a Soul Stone, so he gets to reclaim the thing he lost that he most loved? What do you suppose Skull and Cap said to one another?
6. Could Iron Man have done something less extreme to win the battle and save his own life? I get that in the heat of the moment, he wanted to snap, too, but had he taken a moment to ponder, could he have frozen time with the time stone? Or is that something beyond his scope as a human? Perhaps he did what he knew would work despite the potential cost?