See picture:
How do I make those faces exactly square? Without influencing their orientation, rotation etc. Tried it with loop tools but it screwed it up.
Thanks!
I’d just scale on the Y axis only using individual origins.
Although it is asked to make them perfectly square which that alone would not work, at least without knowing how much to scale.
What may work for this method is to measure the lengths of the edges. Find the length of the horizontal one (horizontal in relation the picture), and the length of the other side. With a little maths, you can find how much to scale it back down so the lengths match.
The maths below should work:
Find the horizontal length and vertical length. (As seen on the picture. You want to shorten the vertical length as I call it)
Find the ratio between the sides,
vertical length / horizontal length = how many times longer the vertical edge is (lets call it x)
So you would need to scale the vertical edge it down by 1/x, so the value from this would make it match.
Which actually finally simplifies to:
horizontal length / vertical length
Easy way, turn on view edge lengths then adjust until the two figures match. 
you could also use a square plane with knife project
then use array to get your overall shape !
happy bl
Mesh tools add-on have an “set edge length” to set absolute length.
Select top/bottom edges with similar and then set the edge length,
repeat for left/right.