Oh you started with those bombs ? Ok so it was your "welcome present" (mine was miyagi, the old man !). But anyway in your page I saw in your inventory that you had plenty of different bombs and actually I can't find any of those base-ball bombs, gold bombs or whatever-else bombs in the shop ! I still wonder where they can be "bought"...
Concerning the option available for one week, well when you go for buying the dragon, bombergod or miyagi for instance, you have on the first page the 1D (1 day) option, and on the 2nd page the same characters with the 7D option. But that seems to be true only when buying characters