1. why eth and arbeth have the same address and why did it go to arbeth and not eth when the person sent me eth?
2. is there any way for me to convert my arbeth to eth without needing to buy more just to reach the minimum amount on exodus?
3. is there any way for me to convert my usdt to btc with some reduced gas fees?
1. As long as it's EVM, then you will find the same address for receipt, not only valid for Arbitrum, but also networks such as Polygon (MATIC), Binance Coin (BSC) & any other network that is compatible with EVM. And why you received $arbETH and not $ETH, it's because that person sent you $arbETH and not $ETH.
2. I don't think there's any other way than to increase the amount until it reaches the minimum redemption limit.
3. AFAIK, You can look for CEXs that accepts USDT on the Arbitrum network for deposits, then you can trade the USDT in the BTC/USDT pair.