In their website bluewallets' lightning experience is described as:
You can use our hosted Lightning wallets or connect to your own node.
Channel
So, if you don't have your own (I guess LND only) Lightning node, I guess you are using a custodial wallet, so your balance is just a database entry behind the balance of a large lightning node controlled by bluewallet team. Your deposit transaction probably did not cause a channel to be opened, but it's just an incoming LN transaction to the bluewallet node which uses their available incoming liquidity.
Invoice
The faucet you linked uses LNurl withdraw to send money. This means that your wallet decoded the lnurl string or QRcode, getting something like https://lightningnetworkstores.com/api/lnurl2?id=C9yU9yPVHW37783hoaDABd
. Your wallet then proceeded to send a get request to that url, which returned some info and a callback URL. Finally your wallet generated an invoice (through the central bluewallet node) and sent it to the server (via callback URL) to be paid.
However I have no clue whether or where you can find invoices in bluewallet.