You will end up with different results depending on which options you select, but people's interpretation of "pot roast" varies greatly, so it's impossible to say if any particular set of answers is "better" than another.
For instance, if you like your pot-roast fall-apart tender, you should shred it before you let it cool down too much. It will be near impossible to get that same texture if the pot roast has been warmed back up.
Likewise, cutting up the chilled pot-roast will result in a much drier, firmer pot roast. It's also difficult to warm back up a whole roast without over-cooking the outside.
Personally, for my preferences (being able to cool it down and reheat it quickly while having succulent meat) -- I would:
Separate the pot roast from the liquid to let it cool. Simply because the liquid is a huge thermal sink, and would make it take much longer to cool down the roast.
Once the roast is cool enough to handle, I would slice it thickly across the grain. (warm enough that it breaks apart some while cooking, but not so much that it shreds entirely).
Place the slices into a container, putting a little bit of the juices over each slice. (to prevent it from becoming dry as the muscle fibers contract; if the meat is firm enough, you can dip each slice back into the liquid, then the storage container).
Store the rest of the liquid separately. If it's a heavy dutch oven, I would move the liquid to some other container, so I don't have to chill down and reheat the pot, too. If you have vegetables in your pot roast that you don't want turning into complete mush, I would put them in the container with the meat.
To reheat, I would heat the liquid first, and then put the slices into the liquid to let them warm through.