Like any other material, Unity will allow you to set tiling negative, to “flip” the texture L/R and U/D (like in your final 4 pictures.) For fun, change offsets (0-1 only) and tweak scale by a tiny amount, and you can make a tiled texture much less obvious.
Rotating (which is in your title, but not what you really want?) is always trickier, such as having x go up instead of sideways.