Is it etiquette to say "allow me" before introducing oneself?

What does "underdog" mean here?

"Underdog" in this video, is a common outdoor children's game. This game takes place on the swings. One child sits on the swing, and another child runs from behind, gives a big push to the swing, and runs under the swing as it goes over her head. Ex: The child gave the other an underdog on the swing set. Ex: When I was a kid, we used to give our friends underdogs when we played on the swings.

Could you explain this humor? I pretty don't get it.

"How long did you think this barbecue was gonna last" is said here as a joke because Ross came into the room with a bunch of luggage. Since they didn't know until he told them that he is going to China, Phoebe made a joke about him bringing all the luggage for the barbecue as though he packed for it thinking it would last for a long time.

What's "is bound to" mean?

"Is bound to" means certain to do or have something, or obligated by law, circumstances, or duty to do or have something. Ex: It's bound to get warmer now that the winter solstice has passed. Ex: She's bound to tell the truth in a court of law.

In what situation do you use the word "roughly"?

You can use "roughly" when you are making a guess or approximation on something. "Roughly" means "approximately" or "around." Ex: She is roughly 152cm tall. Ex: We are roughly fifteen minutes away. Ex: He said he would be here roughly around 12:30.

Can I call new employee in our company “new recruits”?

Yes! A "new recruit" refers to a newcomer to something, such as a job, sport, the military, activity, etc.