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I registered my paypal account when at US. But now I am aboard and I cannot reach my US phone number in a long time. That is, I cannot receive any text messages or phone calls. How can I add a new phone number from other country? Any time it shows "invalid phone number" and I cannot type country code which started with "+".
Paypal is country specific so you have to open a paypal account in the country you reside in and add an address / phone number / bank accounts / cards from within that country.
Using a country specific paypal account internationally will always hit problems as paypal varies so much country to country.
You should really withdraw any funds / resolve issues / remove cards and bank accounts / cancel any subscriptions and close the old Paypal account before you move countries. If you don't then you may have problems doing so once you have moved and may need to contact customer services for help to resolve things.
You can however add a U.S bank account (not card) to 'most' other countries paypal accounts. This is because paypal is a U.S company and so allows this.
You can't register a lot of accounts anyway as you are only allowed a maximum of 2 paypal accounts and only then if 1 of them is personal and the other 1 is business.
There is no 'solution' to your problem, paypal is country specific because it varies so much country to country and thats why you would find it difficult to use a country specific paypal account internationally.
I can only give you the facts on how it works, never solutions to everything is there.