1) I use separate bowl to whip up a lather since the bowls I have for the soap are too small to contain the lather (I just pick up soap with my brush). As somebody commented, if you have cup/bowl large enough, you can lather on puck.
2) My soaps stay in their separate bowls. You can always use just one mug, but then you'll have to switch the pucks wet (might get a tad messy) or remove the soap from the mug after it has dried there. This might or might not be easy depending on your setup. I'm happy with separate bowls (I only have 3 soaps), but you can try out what suits you.