What does "time to shine" mean? Could you give me some examples?

Is it common to say "I'm glad we're doing this." while dating?

It's a common phrase to say when hanging out or doing an activity with someone! So it could be used for dating, or with friends too. Like, if you've wanted to do something with them for a while, or weren't sure, then "I'm glad we're doing this" is a nice phrase to express your pleasure concerning hanging out or the activity at hand. Here, they're not even officially dating, he's expressing his interest in the walk they're on! Ex: I'm glad we're finally watching this movie together! EX: I'm so glad we're doing this. It's nice to have dinner at a friend's house.

What does "it" refer to here?

"It" is mentioned in the sentence prior. It refers to the shortest commercial flight in the world, which only lasts about 80 seconds.

What does "steal the show" mean?

To "steal the show" means to become the main protagonist at an event or some place. In essence, it means to be or perform so outstandingly that you become the "star" (that "steals" the show). Ex: The second female lead stole the show from the main actress. Ex: The rookie performed brilliantly and stole the show.

What does "own up to" mean?

To "own up to something" means to admit or acknowledge your actions or mistakes. It is a colloquial expression that is often used in confrontations or apologies. Ex: I'm sorry. I own up to what I did. Ex: To be a good person, you have to always do your best and own up to your mistakes.

What is "piggy"?

"Piggy" is a somewhat childish, cute way of meaning "pig." In slang, it may refer to someone who is chubby or enjoys eating, but in this context it literally means a young or baby "pig," which may also be called "piglet." Ex: I'm such a piggy. I need to stop snacking. Ex: I need to stop being a pig. I need to start working out.