Yes, I'll grant you that there is more risk of soot in a stove you assemble and disassemble. Every piece of gear has advantages and disadvantages. I find that the soot is relatively minimal, since the stove burns so hot. What does form is all on the inside, so as you take it apart and put it together you can usually avoid getting much on your fingers.
It is possible for ash and embers to fall down from the bottom of the stove, which is why I would always use a piece of foil under it. All my videos mention and demonstrate this. In windy dry conditions, I would form this foil into a bathtub shape to be even more sure that I was preventing anything blowing off the foil.
As far as storage goes, a tin is a heavy item, and could significantly increase the stove weight. This is certainly true for the tin you get with the Pocket Stove sold in the UK. If you really want something with rigid sides for the FireFly, anything that can hold a sandwich like a Tupperware sandwich container would work. But this is not what I recommend you do. Instead, the reinforced tyvek pouch I have available is quite light and serves this purpose well. Plenty of room for a few fire starters, lighter, what have you. I always keep a mini bic and some cotton balls in mine, for example. The tyvek pouch is light, and the whole idea is to keep it light. This is BPL after all. ; )