I think it is better to open a government issued bank account rather than private Banks. Not only the Fees is less in government issued banks but they are trusted enough.
You can manage your banking account online from anywhere in the world where you have Internet access. You can check your balance and other features also it is possible to make online transaction from anywhere in the world
I think the main difference between the individual and company website is that you have to pay more fees if you are having a corporate account if you are having an individual account the fees is very less
It depends of the bank to bank that whether you need to physically available in that country or not. You can either choose central Cyprus bank or pirateus bank
I would rather choose that bank account which have positive reviews on other websites.I would not go with any new one because it is about money. I want to make sure that my money remain safe