It's a story that happened in the past at an airport. It starts this way
When I got to the check-in desk my parents were nowhere in sight. I was waiting for them until it suddenly occurred to me that they had already checked in and they were waiting for me in the departure lounge. This was a real problem because I had given my passport to my mother so I couldn't check in.
I immediately called my parents on their cell phone. I was right they had already gone through to the departure lounge. They were waiting for me for almost half an hour at the gate.
I think for 2nd and 3rd one we can use past perfect continuous cause we are talking about length. But I have doubts in these three bold part.