"second half" or "latter half"?

The number of hits in a google search was as follows:
"the second half of 2004" --> 43900
"the latter half of 2004" --> 2520

Question1: Is "the second half of XXXX (year)" more common than "the latter half of XXXX"? Or is it ever OK to use "the latter half of ..."?

Question2: For "the first half of XXXX", there is no alternative. Is this correct?

"Second half" or "latter half" both are correct but, as your web search has shown, the former is more common. There's a hint at the answer to your second question. Opposed to "latter" we have "former". You might refer to the first half as the "former half". It would also be correct but I'll bet you'll not find as many hits on Google as you would for "first half". The words "latter" and "former" do tend to have a bit of a formal feel about them.