Does each of them has different purpose other than being tied to USD?
For me, if you take closely on their respective prices, sometimes their value is not exacly to 1$, some of them sometimes are more than 1$ or less than 1$. And also, some platform or exchanges offers staking some stable coins with respective percentage based on what stable coin you used.
Do they have different features or the fees when using them is different from one another?
This will based on the network where the stable coin is based, like if you will transact under Ethereum network, then it will become different with other network, like on Solana network or Binance Smart Chain or Tron Network.
Why USDT is commonly used when trading other crypto not the others?
Honestly, if I am using stablecoins on exchanges, it is not matter at all. But the most common I am using is the USD Tether. Since USDT got the much higher volume compare to other stablecoins.