I can't download the Facebook app from App Store

Does it say why it won't? While a missing payment method could be a reason, there is nothing in what you have said so far that indicates that that is the problem. I see you are running iOS 13. Is it updated to 13.4 at least which is what is required for the Facebook app?

This is unfortunately a long list of things to check but you have provided too little information for us to propose a specific solution. When you start your first post describe what happens when you try to download, and the exact wording of any error messages. This would greatly aid us in helping you, and keeping this list shorter and more directed. In the meantime review these suggestions and documents if you think they apply:

Read this article to make sure you know how to download apps and games on your iPhone or iPad

Download apps and games on your iPhone or iPad - Apple Support

Read this document if you can’t download or update apps on your iPhone or iPad --> If you can’t download or update apps - Apple Support

If the first 5 don't help, use the 6th.

If you see a message that says "Your account has been disabled in the App Store and iTunes", follow the directions in this document --> If a message says 'Your account has been disabled in the App Store and iTunes' - Apple Support

If a feature on your device is not working, it may have been disabled. See how to use Screen Time on an iPhone, iPad, or iPod touch by clicking here --> Use Screen Time on your iPhone, iPad, or iPod touch - Apple Support Go to: Content & Privacy Restrictions > iTunes & App Store Purchases and allow adding and deleting apps.

Learn what to do if you can't redownload an item or if you don't see the item in your purchases.

If there's an issue when you redownload apps, movies, or other content from Apple - Apple Support

- Items bought with another Apple ID, and about Family Sharing.

- Incompatible apps.

- Hidden items.

Other considerations:

Do you have the requisite system version for the app you are trying to download?

Do you have the same problem when using a different Wi-Fi network?

Does restarting your device make any change?

Can you download apps normally on another device?

Did you try restarting your device?

Resolve issues between iTunes and third-party security software - Resolve issues between iCloud for Windows or iTunes and third-party security software - Apple Support - You can’t connect to iTunes Store to buy or download content.

Do you need to add a payment method? This document explains how to add a payment method to your Apple ID on an Apple mobile device, a Mac, or a PC --> Add a payment method to your Apple ID - Apple Support

Check Apple's system status to see if a server is having problems --> Apple - Support - System Status

If you can't connect or sign in to iCloud, see if this document has a solution --> If you can't connect or sign in to iCloud - Apple Support

If you can't connect to the App Store, iTunes Store, or Apple Books, read this support article --> If you can't connect to the App Store, iTunes Store, or other Apple services - Apple Support

- If none of the suggestions work, try the last one: "If you’ve tried all of the above steps and you still can’t connect, contact Apple Support."

Click here --> https://support.apple.com/choose-country-region Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service --> "See a list of Apple phone numbers around the world."

Click here --> https://support.apple.com/HT201232

If you can't download, make purchases or update apps, including free apps, you need to update your payment method or add a new one. If you already verified that a payment method is available in your country or region and you're still having trouble, learn more.

If one or more of the following 6 options are true then you can't choose None as a payment method then the Billing information is needed . The "None" option will not appear...

1. If you have an unpaid balance or payment due
2. If you have a subscription that automatically renews
3. If you're using the iTunes Store or App Store for the first time
4. If you are not in the country or region you’re creating an Apple ID for
5. If you changed your country or region
6. If you're a part of Family Sharing