Hello, you can start building the puzzle and if you don't want to continue, you can roll it up and leave it until you continue. It is also meant to hold the puzzle together until you continue.
Yes, you can. It works better if you roll it up rather loosely. After unrolling, you might have to tuft a few pieces again. But basically it works great. It doesn't matter whether you've only put a few or many pieces together. I can only recommend it. :-)
This is the box in which the puzzle mat comes. The "mat" itself (is simply a large piece of thin felt and a plastic roll that plugs together) is larger.