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Can I open bank account in this bank?

US Credit unions and community banks don't work with IBCs. You'll need to go and apply in one of top 5 banks. Or find a EMI.

Have a US EIN for your IBC and intend to deposit 250K for a USD-only account. Multi currency corporate banking does not require more deposit, but is only available from 2.5-5M annual turnover, for example in Wells and PNC. EastWest bank offers multi currency to SMEs, but they stopped accepting IBCs. Could be an option for a US LLC though - make your offshore IBC own the US LLC for this banking option.

The US slashed interest rates recently, and due to "lack of reward", getting a bank account there is not as easy anymore for non-U.S persons.
 
If you want to take some risk, you can try to foreign register your IBC in one of the US state (for instance NM that is cheap with no yearly renewal fee), that will give you a local US LLC. Even if the state certificate will show in its comment that it is a foreign entity, most bank won't know the difference and will open the bank account as a local US entity. You will however have to make sure that you also registered this foreign entity with the IRS to get an EIN beforehand as the bank will expect one.