What does "costing the company" mean?

What is "a lil' birdie"? Does it really mean a bird?

Great question. This is a version of a popular idiom (a little bird told me). It is used to say that the speaker knows something but prefers to keep the identity of the person who told them a secret. It is not referring to a real bird. Ex: A little bird told me we have an exam today. Ex: A lil birdie told me you're thinking of quitting.

How can "sitting around" and "talking" come in a row? Is it "present participle"?

Yes, to "sit around talking" is actually a commonly used expression. It is in the present tense in this video, and is used to describe the act of spending a lot of time chatting casually, without doing anything useful or stimulating. The speaker has used this expression to state that instead of wasting time just chatting, they could go outside and actually do something. Ex: It was a relaxing weekend, we just sat around talking for hours. Ex: Don't just sit around talking! Let's go outside.

Does New York refer to a State of New York? Or New York City? It's hard to tell the difference!

You're right. It is hard to tell the difference! However, I'd say, in general, people refer to the city more than they do the state. So I'd assume that they mean the city. But both would be valid here! Since perhaps they can recognize the area in the state and not just the main city. If the context isn't enough and a clear distinction needs to be made, then "New York State" or "New York City" would be said. Ex: I'm heading to New York City to meet up with a few friends. Ex: I've never been to the State of New York before. Ex: I want to go to Times Square in New York. => through context, we know this is in the city.

What does "roll over" mean?

"Roll over" in this context, means to lay on the ground and turn your body in a way so that a different part of you is facing upwards. You will hear "roll over" quite frequently with dog owners, as this is a command for dogs. Ex: The owner commanded the dog to roll over. Ex: The car rolled over several times after being hit by a semi-truck. Ex: She rolled over to the other side of the bed. Thanks for your question!

Would it be weird to say "of everything" instead of "in everything"?

Yes, unfortunately, only "in" here be used here, not "of." The full expression is to "see the bright side in everything," and this sentence has included this expression. The expression involves the action "to see [x] in [something]," so "of" is not appropriate here. Ex: Mary is always positive. She sees the bright side in everything. Ex: I don't know what she sees in him. (I don't know what she likes about him.)