How can I remove my payment methods so that I am not charged for an application that I delete and want to reinstall?

1.

You cannot remove your payment method.

If you want to make purchases or update / download apps, including free apps, you need to have a payment method on file.

If you don't have a credit card or don't want to use a credit card, you can also use your Apple ID balance as payment method, see -> Add money to your Apple ID balance

Add money to your Apple ID balance – Apple Support (UK)

2.

so that I am not charged for an application that I delete and want to reinstall?

If you have downloaded a paid app, you must pay.

Even after you have deleted the app, you still have to pay.

If you do not pay, you wiil get a message like this -> If a message says 'billing problem with previous purchase' or 'verification required' -> If a message says 'billing problem with previous purchase' or 'verification required' - Apple Support

• If these messages appear, you might be unable to make purchases, download free apps, or use subscriptions. To fix the issue, change your payment method. If you can't change your payment method, you can redeem a gift card and use the balance to pay for any unpaid orders.