Flash loans are useful for both arbitrage and loan liquidations. Every swap on Uniswap and its many forks on many chains is actually a "flash swap" under the hood - you can take the coins out and use them before the code checks that you have sent the tokens for the swap in to the contract. You don't even need a dedicated flash loan provider on a given chain to be able to use very large amounts of capital sitting in DEX pair contracts.
There are other case-specific uses for them, but loan liquidations and arbs are the big ones.
Depends on your use case. First, AAVE is on ETH, and most arbitrage profits are on other chains. For example, there aren't a lot of flash loan providers on BSC (Binance Smart Chain) with deep liquidity, so everyone just uses flash swaps. The most profitable chain for arbs is BSC (binance smart chain). If you're using the loan for DEX arbitrage, then there is no point in using a third party loan provider like AAVE. You have to pay swap fees regardless, and a flash swap is "free" in the sense that you only pay the swap fees for the coins involved, and you must pay them whether you send the coins to the contract first, or if you borrow them and pay them back at the end.
So if you bring in outside money from a place like AAVE for a DEX arb, then whatever fees you are paying to AAVE are an extra, optional expense, since the swap fees must be paid regardless.
There are other case-specific uses for them, but loan liquidations and arbs are the big ones.