Can't send a gift card through App Store

You can have a credit card / debit card on file and an Apple Account balance.

If you have set your Apple Account balance as your default payment method, your default payment method will be used first by Apple when you need to make a payment.

Some purchases might require you to have a credit card on file, even if you use your Apple Account balance to make the purchase.

See -> Gift apps, music, movies, and more from Apple

Gift apps, music, movies, and more from Apple - Apple Support

• 👉 Gifts are billed to your payment method, not to your Apple Account balance.

Check also -> If your payment method is declined in the App Store or iTunes Store, see -> 

If your payment method is declined in the App Store or iTunes Store - Apple Support

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How to complete your purchase if a payment failed or was declined

1. On your iPhone or iPad, open the Settings app.
2. Tap your name.
3. Tap Payment & Shipping.
4. Add a different payment method and remove the old one. 
5. Try to complete your purchase.

If you still can't make a purchase

• You might have an unpaid order. Learn how to pay an unpaid order.
• Contact your financial institution. 
  • You might need to ask your financial institution to allow international purchases on your debit or credit card.
  • If you want to know why a debit card, credit card, or other payment method was declined, speak with your financial institution. Apple doesn't have information about why the payment method was declined.
• In some countries and regions, your payment method might be declined because of changes to local law. Learn about billing and purchases in Europe or what to do if your card is declined in India.
• Still need help? Contact Apple Support.

If you have followed all the steps and instructions and if you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.

1.

Moreover I got 4 Apple ID accounts closed permanently one after another because of the trials I made for purchasing, in addition that each of these ID’s was having some amount which I added whenever I create any account and all gone waste.

Not sure why you use 4 Apple accounts.

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.

See the following Apple articles

Sign in with your Apple ID -> Sign in with your Apple ID - Apple Support

Manage and use your Apple ID -> Manage and use your Apple ID – Apple Support (UK)

2.

also I tried adding different payment methods other than mobile number, was accepted in adding the payment method

If you use mobile phone billing as an Apple ID payment method, contact your carrier. Perhaps you need to add funds to you SIM card balance.

3.

but still declined at the checkout stage mentioning one message that “unable to finalize your purchase as of now, contact iTunes Store support team to finalize the purchase”

The you need to get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service or check -> here for more support and assistance.

We can't help you, we are also users of Apple products & services like you.