Traveling from Germany to Italy with rental car

You can cross borders easily but the drop fee is the problem. It’s good that you know about it. We were quoted 1000 Euros so got more creative using a taxi to cross border, picking up another car.

Five days?!?
Please tell me that is a typo.

OP trip is 4/27-5/13
So I am assuming it’s a 15 day rental-at least I hope so

Glad you are aware of that big drop off fee. Not sure I would have gone down that road instead of using separate rentals in each country, with a short train trip across the borders. But to each his own.

Assuming you will be spending nights in towns or cities along the way, you need to be aware of the scarcity of parking in many places and the cost of parking once you find it. Don't count on any hotel having their own parking lot. Have an IDP for each driver. Know the rules of the road in Italy. Know about speed limits and photoradar, bus lanes, ZTLS, tolls, the difference between diesel and gasoline pumps at gas stations, the dangers of leaving personal belongings in the car any time the car is unattended.

If you have any car troubles, you deal with whatever car rental company you are using. Gemut appears to be a middle-man, so your rental agreement should state which company you are actually renting with. Read your rental agreement carefully. Depending on which insurance coverage you selected, lots of things may not be covered: glass damage, theft, injuries to people, etc. If you did not select insurance, you pay for any damages, unless your credit card offers car rental coverage, and that may be limited. You may have a deductible.

To clarify...the rental is for five days, it's just a portion of the trip. Thanks for suggesting to get creative with taxis, that might save me the $800 drop off fee. I have contacted the hotels in Hall and Assisi and they both offer parking. We have rented a car in Italy before but not crossed borders.

For a 15 day trip, I'd agree the drop-off fee is worth it. For a five-day trip,, you'll just be doing a lot of driving.
I like to approach trips like this from either end. Do you get to stay and enjoy Naples after dropping off the car? Once you pick up the car, will you immediately be departing Munich? Are you just stopping once in Italy?

I know the trip seems a bit strange but we are visiting "our exchange student" that lived with us 12 years ago, so the trip begins in Munich. On a previous Italy trip we did Rome, Tuscany and Lake Como regions, this time we wanted to see more of the coast so the itinerary developed from there: Munich(3 nights), Hall (2), Assisi(2), Sorrento(4), Capri(2) and Rome (3). It's a whirlwind thinking of dropping staying in Capri for just a day trip giving us an extra day in Sorrento. Boy, did I go off topic.

You might take a train from Munich airport to Innsbruck and rent a car there for use in Austria. Advantage is it will have an Austrian vignette already attached.

Then turn the car in at Innsbruck and take the EC train to Bologna and rent another car there. Saves drop fees, gas and tolls.

Just so we understand, you will drive from Munich to Hall, stay two nights, then to Assisi for two nights, then drop the car when you arrive in Naples? At the airport or in the city? You'll need to be very careful with your driving instructions if in the city to avoid the ztl (and the general Naplesness of Naples).
I believe cars in Austria need a vignette, so make sure you get that from the rental agency (or instructions on where to get it). In Italy, the main issue is parking and ZTL.