ok so my question is what happens to Kate if you actually do kill that messed up dude that you are looking for during the whole game?

************SPOILER************************************************************




She gets shot accidentally by Jimmy Pegorino.

I think you're confusing things a little.

<SPOILERS>
The "special someone" you're looking for is actually Darko Brevic, the man who sold out your old army unit. Killing him makes no difference to Kate's fate in the storyline. It's whether or not you kill Dmitri that determines whether Kate lives or dies. If you kill Dmitri, Pegorino accidentally kills her in a drive-by shooting at Roman's wedding. If you do the deal with Dmitri, Kate refuses to attend Roman's wedding with you. But she will call you to offer her support after the Deal ending.
</SPOILERS>