Shard of Minium is occasionally dropped by aggressive mobs. When combined with an Inert Stone it can be used to create a Minium Stone, which allows for item transmutations. The shard otherwise has no uses.
Note that this shard has nothing to do with Soul Shard.
The Philosophers stone is a currently uncraftable item with the exact same properties of the Minium stone, but with more durability.
The Alchemical bag is a currently uncraftable item which can carry 104 stacks of items. There are 16 (for the different colors of wool) different types of alchemy bag. Alchemy bags of the same colour all share the same inventory, when used with one player.