What kind of artist is "cabbie-artist"?

What's "ditto"? What does it mean?

"Ditto" means "same here" or "as has been said before." This is an informal expression that is used when you want to express that you feel the same way about something, i.e. when something already mentioned is applicable again. Ex: A: I hate when it rains. B: Ditto. Ex: A: If she cancels our plans one more time, I'm going to stop talking to her. B: Ditto.

"Ginger ale" and "gingerbread", is ginger a common ingredient for American cooking?

No, not really. "Ginger" is more of an exotic ingredient in American cooking. We tend to use ginger when baking certain things like cookies or if we are cooking certain Asian cuisines.

What does "silly game" mean?

A "silly game" in this case refers to being in a confusing situation where two people are acting like they are in a competition and being in a game, and it is silly, or pointless. In English, sometimes confusing situations between two people are referred to as a "game", especially when it involves a romantic situation. Ex: I'm tired of these games. Does she like me or not?

What is "Slurpee"? Is it a brand?

You are correct, "Slurpee" is the brand name of a slushie (frozen carbonated drink) that is sold in 7-Eleven convenience stores around the world. These drinks are self-serve, so you can make diverse flavor combinations for your Slurpee. Ex: It's so hot out, wanna get some Slurpees from 7-Eleven? Ex: My Slurpee is so cold, it gave me brain freeze.

Is it okay to not have verb in this sentence?

In this conversation, it is understood that she meant "What easy way are you talking about?" The phrase containing the verb ("are you talking about" - talking is the verb) is implied. However, the sentence she says is not a complete sentence since it doesn't contain a verb.