Do you really need the result to be
"" in the false case? If you only need the cell to look blank (e.g. you won't use something like
=ISNUMBER() on it later), you can use conditional formatting to hide the contents in the false case.
The conditional format you'll apply to the cell so that it doesn't display anything is the custom format
"", like this (it's in Portuguese but you get the idea):
The formula in the cell will be, as expected, simply
The conditional formatting formula could be
=!X!=0, but that would force recalculation of
!X!, which you don't want (your "Point 2"). It's better to harness the cell itself by using
=B1=A1 (supposing our cell is B1) -- that would imply
!X! = 0.
Even if you need the cell content to actually be
"", usually minor alterations can be made in the worksheet so that this approach can be used. If that's the case, leave a comment describing the situation.