I live in Israel,my Google Play country is set to USA. How to change to Israel? The need to change the above had arisen when I tried setting up Family Link on my kid's phone, which fails due to" country setting being different on parent and child phones". Sure enough, his country is set correctly in Google Play settings.

How can I change mine when the account->country and profile setting appears unchangeable?

Edited for clarification: I have never lived in the US and don't recall setting the country to US. I have no US based payment methods defined , but I do have Israeli payment method defined and used.
You have good instructions here:
https://support.google.com/googleplay/answer/7431675?hl=en .
But since this is Google you need to add payment method.

Change your Google Play country
If you move to a new country you may want to change your Google Play country. Your Google Play country determines what content you see in the store. The apps, games, and other content in the Store can vary by country.

You can only change your Play country once per year. So if you change your country, you won’t be able to change it back for 1 year.
When you change your country, you won’t be able to use your Google Play balance that you have in your old country in your new country.
Change your Google Play country
To change your country, you need to set up a new country in Google Play. To set up a new country, you must be in that country and have a payment method from the new country.

On your Android phone or tablet, open the Google Play Store Google Play.
Tap Menu Menu and then Account and then Country and profiles.
Tap the country where you want to add an account.
Follow the onscreen instructions to add a payment method to that country.
The first payment method must be from the country you’re adding a profile for. Once you create the profile you can add payment methods from other countries.
This creates a new Google Payments profile linked to the new country. The Google Play Store will automatically change to the new country. It can take up to 24 hours to change.

If that is not working:
Fix problems changing your Google Play country
If you can't change your Google Play country or don't see the option to, try the following:

Clear your cache and data
On your phone or tablet, open the Settings app Settings app.
Tap Apps &amp; notifications and then See all apps.
Scroll down and tap Google Play Store Google Play.
Tap Storage and then Clear cache.
Tap Clear storage and then OK.
Check if your app is updated
Open the Google Play Store app Google Play.
Tap Menu Menu and then My apps &amp; games.
Games with an update available are labeled "Update." You can also search for a specific game. 
Tap Update.