The Apple Card doesn't send a bill but there is a monthly statement at the end of each calendar month. The statement is available on the 2nd or 3rd of the following month and they should be sending you an email notifying you. The statement is available at https://card.apple.com/ or if you have an iPhone, open the Wallet app, tap the Apple Card, tap Card Balance. See: Download or export your Apple Card statements and transactions - Apple Support
To use the Apple Card to purchase an iPad you can use Safari from an Apple device where the card is in the Wallet and it should give you the option to use the Apple Card and also give you the interest-free Monthly Installments option. If that isn't possible, you can call 1-800-MY-APPLE to make the purchase and let them know that you want to use the Apple Card and also the interest-free Monthly Installments. See: Apple Card - Monthly Installments - Apple
Regarding the app that used the card, if you don't want apps to charge the Apple Card, change your default payment method (it will be the top one in the list if you have more than one). To change it, see: Add a payment method to your Apple ID - Apple Support
Apps will charge renewal fees if they are not cancelled before the renewal date. There is an Apple article that explains how to cancel subscriptions. Click on the following link: If you want to cancel a subscription from Apple - Apple Support
To try to get a refund for the unwanted renewal, see: Request a refund for apps or content that you bought from Apple - Apple Support