Non-US Citizen Corporation

I'm not-US citizen that want to incorporate C-Corp

This is not a problem. No-one cares about your citizenship when you open a corporation.

However, there are a couple of problems hidden here:

I will fly to US in order to open US bank account

You cannot do that. You won't have signature authority (as non-employee).

My company should based on advertisements as primary income.

Advertisements don't just appear. Someone needs to market your advertisement space, some one needs to create that space to begin with (you're assigning ownership over your billboard? Internet site? Who's making these? Maintaining?)

That leads to the next issue:

I'm not intend to hiring permanent staff and the corporation only have one director which is me.

Director doesn't make day to day decisions. So you have to have someone who does. You have to have at least one executive officer (also known as CEO) in your corporation which will be responsible for day-to-day operations. This officer must be an employee. That officer cannot be you (unless you get a working visa to US). You will have to hire someone.

My question is, what kind of taxes my corporation and I need to pay? Do I need to pay tax at all?

You will pay these taxes:

1. Income tax on your worldwide corporate income
2. Payroll taxes on your employee(s)
3. State taxes (if any, depending on the state)
4. Franchise taxes (if any, depending on the state and the operations)
5. Foreign income taxes (if you have income in a non-US location - you'll have to pay taxes there too)
6. Sales taxes/VAT (depending on the place where you make your contracts).

And of course, any money you distribute to yourself from the corporation is taxed as your personal income in your country of residence.

First of all, no bank is going to give you an account in the US unless you are a resident.

But to answer your question; your company pays tax in the country it was incorporated in (US). You then pay tax on any income to the resident country.

(ps. Im not a lawyer)