First of all DEFINITELY get a guidebook and study up. I recommend Rick Steves' guidebooks. The great thing about them is that in addition to recommending itineraries and attractions, he also gives a lot of practical advice, like how to buy tickets, how to ride public transportation, where public restrooms are, how to order food, etc.. Since you have not been to Europe before, you need the practical advice.
Have you flown before, or just not to Europe?
I bring snacks with me all the time when I travel. Packaged stuff like you want to bring is fine but you can get those things in the supermarkets there. Peanut butter is definitely subject to the TSA "liquids" rule so it would need to go in your checked bag.
You will need to ride public transportation in Berlin, at least some of the time. Go on YouTube (or have your daughter do this) and type in "how to ride public transport in Berlin". Find a video that was made in the last couple of years and watch it, several times, to familiarize yourself. It is easy (and fun!) and cheap to ride but don't show up in Berlin and try to figure it out there.
I (female in my 50s) have traveled to Berlin solo four times. It's very safe. But just like you wouldn't cross a dark park in an unfamiliar neighborhood at home, don't do it in Berlin. In what part of the city are you staying?
Also:
Check on your cell phone plan and make sure it includes international data (or look into how you can add that to your plan). A lot of English is spoken in Berlin but the Google Translate app comes in very handy when you are, say, reading labels at the grocery store. Do not depend solely on wifi while you're there. Google Maps is also very handy for public transit schedules and navigating.
When you're ready to depart you'll do pretty much what you do in the US when you're flying. You'll check in (download your airline's app). You'll scan your boarding pass and go through security. Your carry-ons will go through the scanner and you'll go to your gate. Is there something specific you want to know?
Again, YouTube is your friend. You can find videos on just about anything travel related. How to go through security. How to get from the airport in Berlin to the city. How to ride the bus. What foods are popular in Berlin. Basic greetings in German. Top attractions. You name it. Please do lots of research, it'll greatly enhance your trip.
Berlin is a wonderful city with so much history, literally everywhere. It's my favorite city ever and I'll never run out of things I want to do and see there. I hope you and your daughter have a wonderful time!