Say I have 8500 euros as hard cash in USA. Can I just walk into a bank and deposit it in my account as US dollars? Is there a limit on how much hard cash I can exchange at once in the states?
Banks only accept US dollar denominated notes, unless they explicitly have a foreign exchange policy. Otherwise you will have to go to a foreign exchange company, they are often set up in airports but they are in odd places too.
You will get a bad exchange rate and an expensive fee. But the more you have, the lower the exchange rate and the fee will be.
Bank of America account holders can exchange foreign currency (no coins) for U.S. dollars at a full-service banking center. Add a currency to view the currency exchange rates for that country and find out how much your foreign currency is currently worth in U.S. dollars.
This would be similar in other big banks too, I imagine. However, the exchange rate might be bad.