I don't fully understand this one (or any of the related issues, probably), but here goes:

Scenario 1:

1. Place a brewing stand and fill fuel and ingredient slots
2. Fill your whole inventory and hotbar with items (different from the ones you put for fuel and ingredient), but leave the 9th hotbar slot open
3. Try to shift-click an item out of the fuel or ingredient slot, it will not move into the open hotbar slot
4. Drop the item in the 8th hotbar slot, shift-click an item out of the fuel or ingredient slot, it will now move into the 8th hotbar slot - so far I have not found any way to shift-click an item into the 9th hotbar slot

Scenario 2:

1. Place a brewing stand and fill the ingredient slot
2. Fill your whole inventory and hotbar with items (different from the ones you put for fuel and ingredient)
3. Shift-click the item(s) out of the ingredient slot, they will go into the fuel slot. Shift-click the item(s) out of the fuel slot, they will go back into the ingredient slot

Scenario 3:

1. Place a brewing stand
2. Place two blaze powder in the fuel slot (one should be used)
3. Make sure that the ingredient slot of the brewing stand is empty
4. Shift click the blaze powder

Scenario 4:

1. Place a brewing stand
2. Place two blaze powder in the fuel slot (one should be used)
3. Place one blaze powder in the ingredient slot
4. Shift click the blaze powder in the ingredient slot