No, you will not. Income earned withing your 401K is not taxable to you until you withdraw it. If you took a withdrawl you will pay tax on that, but it will not be reported as dividends.
No. You will not receive a 1099 on dividends in your 401K account. Those are not considered taxable income until you make a withdrawal from your 401K account. Your dividends will be listed in your statements but you will not receive a 1099 form.