No. Each year is completely separate. What you owe for last year doesn't affect this year.
No. Federal tax you paid is not deductible on your federal tax return. There is a handful of states in which you can enter federal tax that you paid.
There are several states that allow you to enter the federal tax you paid on your state return--Alabama, Iowa. Missouri, Montana, and Oregon. If you are filing in one of these states watch for the deduction when you prepare your state return.
No.
I assume you mean under itemized deductions on Schedule A. State and local taxes are deductible (limits apply), but federal taxes are not.
If you paid estimated taxes for the current year's return, you will apply those payments towards your tax liability, but that is not a deduction.