Question:
1. A country with a reputable bank, non tax and allows non residence to open an account. Does it exists?
I think Swiss bank offers bank accounts to the foreigners upon completion of mandatory requirements. They are famous for keeping the secrecy of their client's information. I am not sure, whether it will help you or not ?
Agreed with you, Swiss bank is one of the trusted bank in the entire world for maintaining security and anonymity of the account holder. I heard that, there are some strict rules and it is difficult to open an account with them.
Swiss bank secrecy is not what it used to be. It's been under fire for a couple of years now and it seems that starting this year it has finally fallen:
https://www.ft.com/content/890a4262-c795-11e6-8f29-9445cac8966f
https://www.swissinfo.ch/eng/business/tax-evasion_swiss-say-goodbye-to-banking-secrecy-/42799134