Translation Confusion

I frequent see translations in lessons that do not seem quite right and  make me unsure of what I thought was correct. 

Here is an example from lesson 5.7: 

One more:

In lesson 5.7, "ci vediamo presto" is translated as "we will see each other soon". 

Since Vediamo is the present tense, the meaning is simply "we see each other soon".  Is "Ci vedremo presto" we will see each other soon?

Hi JackK15, 

Thanks for your questions!

Let me start from the first one: "Aspettando il tuo arrivo, ho parlato con Maria."
This was translated with "While waiting for you to arrive, (I) spoke with Mary."
In this case, the English text conveys the same meaning but it is not a literal translation.
In fact, you are correct: "il tuo arrivo" means "your arrival". In this specific case, we have opted to update the English translation with "While waiting for your arrival..." as you suggested, as it allows to refer to each corresponding bit in the Italian sentence more easily.

Concerning the second phrase "Ci vediamo presto": although you are correct, and the phrase is in the present tense, it really means "We will see each other soon", as an informal greeting (stating you will see the other person really soon). For instance:
"Grazie per la cena, ci vediamo presto!" - "Thank you for the dinner, I'll see you soon!"

Please note that "Ci vedremo presto" is slightly different as it is not usually used as a greeting but simply when you want to make clear that you will manage to see each other soon. For instance:
"Ci vedremo presto, il 5 novembre" - "We will see each other soon, on November 5"

Hope this makes it clear but let me know!