Can I keep my US address and accounts after I leave the country?

You can keep the accounts, but be honest about the address. Maintaining a U.S. mailing address (a trusted relative, a friend, or a mail-forwarding service) genuinely helps, you'll still receive tax forms, cards, and statements, and some firms are easier to deal with for "domestic" customers. However, you should not misrepresent your residency: tell your brokerage and IRS your true status and file Form W-8BEN so withholding is correct. Banks and brokerages may restrict or close accounts for nonresidents, so confirm each firm's policy before you go. Keeping at least one bank account and a credit card open also preserves your U.S. credit file in case you return. The rule of thumb: keep useful infrastructure, but never lie about where you live.