You mean 1 November 2023, right?
Broken record here, but below I'm linking to 2 major sections of this Rick Steves website that could be very helpful in your planning.
Travel Tips covers most of the basics on traveling in Europe. Although the group you're volunteering with should provide a lot of this kind of information specific to working with them, this section can help with what they may not think to tell you as well as informing you about what you need to know that you didn’t know you need to know. https://www.ricksteves.com/travel-tips
The Explore Europe section can get you started with what to see and do in Germany and especially in your specific areas of interest. You can also find basic info on other countries. This link is to Germany: https://www.ricksteves.com/europe/germany
Another very important resource is the Man in Seat 61 for information on train travel in Europe. This is the part titled A Beginner's Guide to Train Travel in Germany: https://www.seat61.com/train-travel-in-germany.htm
To advise on what is budget friendly, knowing the budget and what it would be for would be helpful. Being unsure of what your budget needs to cover, I'm going to recommend that you use Booking.com to look for accommodations which could be the most expensive part of any excursions away from where you will be staying most of the time.
About what to pack, it will be winter -- cold, dark and quite possibly snowy. Take a look at timeanddate.com and search for actual historical weather data for the past few years in Munich and Augsburg to get an idea of recent weather trends. When I lived in Nürnberg in the early 80's it was like I described above. It could be different now 40 years later.
Assuming you won't be on a farm outside of town, there will be restaurants and shops wherever you are. Your aunt and the other mission folks should be able to help you with that. Googling something like Bavarian cuisine will give you lots of information to drool over. Add a city name and there will be specific restaurants to explore. Keep in mind that there will also be restaurants from other European countries and other parts of the world. Even 40 years ago, there were Italian, Chinese and Greek restaurants in Nürnberg. In fact, there was a Greek restaurant a block from my apartment that specialized in food from Crete.
I hope everything works out for your trip, and I'm glad you've already been informed about Schengen. Please be mindful of the advice to plan to leave the Schengen area earlier than day 90 in case there is some delay in your departure.