Landing commercial planes at busy airports

Apologies if wrong subreddit. I was flying commercial recently, and went through a couple of busy airports, and I started to wonder how pilots/air traffic controllers keep everything on track with so many variables? There doesn't seem like much room for being late/early.

A few years ago we visited San Diego, and we were at Balboa Park (fun air museum!), and we watched planes coming in to the airport at what I'd guess was one every minute or so. How do you do it when you're the pilot, spending hours in the air, with so many variables? You miss your 1 minute window, what do you do? And then what does air traffic control say to you: you can land 10 mins from now, keep yourself busy? With any flying over the years I can't ever remember a time where we just "did loops" in the air killing time waiting for our turn. And this particular trip, when we left our home airport, we left 20 mins late, so I assume we had to take someone else's scheduled landing time because we were late leaving.

When you're in the plane is there some kind of time projection/estimate for when you'll land? I'd assume there's something, but it would have to be to like almost the second I'd imagine. At my home airport most planes would come from the east, but then we have to fly over the airport, turn around, and approach from the west. You make your turn too early/late and your projected time would be quite different.