How do I transfer BTC from my Coinbase account to my Android wallet? When sending BTC (funds) from the Coinbase website, it asks for a bitcoin address to which to send it. What is one supposed to do, type it in?

What I would like to do is display a QR code in my Coinbase account that I scan using the wallet on my phone. My phone then sends a funds request to Coinbase which is displayed in my account. Then I simply send the funds.

I prefer using the Android Bitcoin Wallet instead of Coinbase wallet.

It seems like Coinbase at one time displayed a QR code for requesting funds from your account. I can't imagine how this might be implemented. Is it even possible?
Yes, type it in. Or you can copy the address and email it to yourself and copy and paste it from the email. 

There really isn't any easy mechanism in Bitcoin for the person receiving the funds (i.e. your phone) to request the money from the person sending the funds (i.e. Coinbase). There is the BIP 70 payment protocol but that requires both a compatible wallet on the sender's side and some webserver setup stuff on the receiver side. Even with that, there isn't anything for the sender to initiate the transaction at all, only the receiver.