If I bought bitcoin on coinbase 3 different dates, do I have 3 different private keys?
No, Coinbase doesn't have private keys if you bought BTC from Coinbase at different dates and times you will get all of your bitcoins in one or in total.
Sample, you bought 1 BTC yesterday and bought 1 bitcoin today so you will get 2 BTC in total and it's not separated.
(You might be talking about input and output?)
When I transfer from coinbase to hardware wallet can I transfer all bitcoin at one time or do I have to transfer the same amount for each buy on coinbase?
Yes, you can transfer all the total amount from your Coinbase wallet one time you don't need to separate them when sending it to another wallet.
If you receive it to the new wallet you'll receive it as a whole bitcoin.