Question regarding standard deduction & capital loss

Hi, I want to know that does the deduction also drops you to a lower tax bracket. For example: my income is $30,000 for 2020. My original tax bracket is  10% for up to $9,875 and the rest is 12%. So the $12,400 federal standard deduction lower my $30,000 taxable income to $17,600 taxable income and my tax bracket will be $9,875 (10% Tax) and the rest is 12% tax is that correct? 


also, regarding state standard deduction? So the $12,400 is only for federal the state has its own standard deduction right and if so what is New York states standard deduction?

 

lastly, regarding capital loss. So I can use $3,000 to offset my income. So can that be combined with other deductions like the standard deduction?