Hello,
If I get it right, you need to show that web part only if at least one of those three querystrings are present. If so, then you were very close with your second example. Please use the following one instead:
{%
if (QueryString.GetValue("a")==null && QueryString.GetValue("b")==null && QueryString.GetValue("c")==null)
{return true;}
else {return false;}
%}
Where a b c are your querystrings (like searchdate).
Best regards,
Jan Hermann