If both transactions make it into the same block you can't really discern which transaction came first, so with the targeted average block interval being 10 minutes you have a bit of leeway with how fast your bot has to react.
You don't really have a guarantuee that both transaction make it into the same block though or that your transaction gets confirmed earlier, however having a higher transaction fees increases the chance of your transaction being prioritized by miners.
No It does not work that way, transactions are included in blocks and if your bot detects the address has already sent the transaction, meaning it has received at least 1 confirmation, then even if you prompt your system to send some bitcoin to the address at the time of notification, the network delay would have its effect and every new block has a delay of approximately 10 minutes before it is mined and it may be longer if there is higher network difficulty in finding the valid hash to confirm the transactions in the new block.
It depends on how the bot detects the transaction. If the bot is checking the blockchain it would be too late, but usually you'd monitor the mempool for a case like this.