Is it a requirement to change credit card and billing address to updated Apple Account country if I am a legal resident in both countries??

If you are not planing to buy content which is only available in the other regions/country, you can still use your US Apple Account and the payment information while abroad.

But, if you want to download content from the AppStore or other Apple Services, which can not be bought in the US, you will have to switch the Apple Account completely, as described in this article:

Change your Apple Account country or region - Apple Support

And your payment information has also be country specific, pointing to your residential address in this country.

Yes, the US credit cards in the wallet will still work for payments in stores, for example.

Only payments directly for Apple Services and content can not be made anymore, if your Apple Account payment information has a different credit card listed.