1. Do I get taxed 15% for the first $30,000 and 25% for the rest?=======correct; Your tax bracket is the rate you pay on the "last dollar" you earn
If so, could you point me to the IRS document that describes that?======== http://www.irs.gov/pub/irs-drop/rp-13-15.pdf
If not, the system seems pretty unfair because my salary increase came in end of the year and I'll be paying the higher rate for the entire year.=======I guess your salary increase already reflects annual inflation rate in it.
2. I'm on the very margin of the tax bracket. So does applying the personal exemption (say $3000) bring down my income from $32,000 to $29,000 hence change my tax bracket?=====of course;personal exemption deduction lowers your taxable income and tax bracket.