I'll share my experience so far. Note that I haven't yet washed it, so I can't comment on that bit (which I accept is pretty critical! Hopefully someone else can shed light on that)
Yes, the layers stay together, very well. The top layer is bigger than the bottom but not by much, so lining them up straight is a bit tricky. You don't have much margin for error, I swore a lot as every time I thought I'd got the top straight and unrolled it, the bottom was showing at the far end. But I got there eventually, and it it hasn't shifted since.
Ours is on a hard floor, and while the bottom layer does grip safely in that you won't slip on it, it does move about more than I am completely happy with - I end up moving it back into position quite a lot. This is my only real complaint.
It's very flat pile, which I knew before I ordered, but I think is worth pointing out as if you want a nice thick plush rug, this isn't it. The more cushioned bottom layer might help, but we don't have that one - the thinner one is fine for our needs though.
Delivery was a pain and quite badly delayed. This wasn't strictly speaking Ruggable's fault, because it was UPS that mislaid it while in transit at Charles de Gaulle airport. However, it's worth knowing that they are based in California, so even if delivery is smoother, there is still an extra chunk of time on the end after you get notified it's been shipped because of the distance.