Nope. Dollars and euros can be held in physical form as paper bills and metal coins. No bank is required for that.
Yes, that would be a decentralized exchange, albeit a rather cumbersome one.
"Decentralized" doesn't mean "zero-risk". Whether it's cumbersome or imperfect is immaterial. Using paper bills and metal coins is the only way to implement a fiat-to-crypto/crypto-to-fiat decentralized exchange because it's the only fiat payment method that eliminates the need for an intermediary, avoids counter party risk, and is the one that is most difficult to reverse. Any fiat payment method involving a financial institution is by definition centralized.
Makes sense. However, if using paper bills and metal coins is the only way to implement a decentralized fiat-crypto exchange then I would think that decentralized exchanges will remain a minority and never supplant centralized exchanges like Bitstamp. For example, I live in New Zealand and the nearest person willing to sell cash for BTC or BTC for cash is located 900 miles away. Therefore, a centralized exchange or an exchange with centralized elements would be necessary if I ever wanted to buy or sell BTC.
Now, if BTC adoption were widespread enough to the point where most people had some BTC then I could see how it could work. But that's really no different from the usual buying and selling of goods and services. After all, if I sold you 5 pencils for $10 in cash then that's decentralized too.