Could you tell me once a mining rig is set up and linked to mining pool, is the daily payout in real world currency or tiny fraction of BTC?
It should be in bitcoin. Back to 2014 when i first try mining, all the pools pays in bitcoin and i can't tell if this may has been changed over time that pools may add more payment options. You can find payment details in the TOS page of the pool without the need to post a question.
Can the payout link into your coinbase wallet?
It will be required to add a bitcoin address to receive your payment. No one will ask you from where you got that address. Coinbase gave you that address as a deposit address but actually you aim to use it like a personal wallet. Keep in mind that it's better to receive mining payment to your personal wallet before deposit them to your exchange balance.