the simple way to see if your 2 in by 2 in works is to set your program nudge to 2 inches, clone the tile and then nudge the clone - do they line up - they do, but as keith said there is grey line visible which is a flaw in the tile fill - also, the tile must not have an outline yours do not so that is ok

I would be tempted to build up the pattern this way and then crop it to the size I wanted

if you are syncing it to an existing square, make sure the square is fill only and no outline, use the coordinate x/y values on the select tool info bar as reference, that way you may not even need to snap

if you resize the tile itself enter actual [identical] values for hight and width, do not rely on percentages etc