Mining - There would be a supply of packs that could be bought off the market place. (unless the market runs dry due to popularity, which would be similar to a print run being over)
You stores dont actually have to mine the packs, they can just sell packs that have already been mined by other people. (or players can buy from those people and not the store). There are a few ways to deal with this but it's not really part of this "limited" (lol) discussion .
As for a player buying a pack and opening it.. yeah.. in hearthstone it would just go straight into your collect. Maybe we consider a tag that allows you to mark a pack so the wallet/card manager knows the pack is being used for draft, and it handles the cards differently.
I envision it happening something like this: Players buy packs, players open packs in wallet for draft (they retain ownership of all cards they opened), players print and cut cards opened from those packs. (yes, they will see the contents of their packs). The player would choose one of the 3 (or 4) stacks of printed cards from the player to the right of them and draft from that stack, and then continue to pass it to the left like a normal draft
(You have the players pick the pack at random since they don't know their neighbors cards. You want to prevent the opener of the packs from choosing which pack to start with)
Draft continues in this way as normal and you deck build. You dont own the cards you play with, only the cards you opened.
I feel like we want the store to do as LITTLE as possible. The more required by the store, the less they will want to run events.