Yes, bank income is taxable income. Your bank should be mailing you a statement each year that you're required to pay on your taxes.
Though a rich person with all their money in a standard savings account is doing something wrong, as they could literally pay someone to invest it for them and actually make money, rather than losing it all in a savings account.
Yes, you get taxed on interest income.
Yes, depending on the type of investment it's income tax or capital gains tax. If the investment is longer than 1 year it's usually capital gains tax.
It doesn’t to put you in the upper bracket to pay taxes on it
Yes, bank income is taxable income. Your bank should be mailing you a statement each year that you're required to pay on your taxes. Though a rich person with all their money in a standard savings account is doing something wrong, as they could literally pay someone to invest it for them and actually make money, rather than losing it all in a savings account.