Uff, you are right, hint about search form is missing
Just open skins/Killer/styleTemplates/global/index.tpl and delete {SEARCH_FORM}.
Session box {SESSION} (Welcome and Login, Logout, Register) will be here, but with a gray background. This depends on style class sessionBox (<div id="sessionBox">).
You have many possibilites where will be session box placed, remaining on place but with different class or........right, left side with additional definitions (send me a msg if you want any help about) .
Milos