I recently bought an older house, and the toilet tank is leaking. In exploring the issue and googling around for toilet repair, I saw no mention of one of the parts that is in my toilet tank. Within the tank, there is a smaller plastic container that surrounds the flush valve. It seems to restrict the amount of water that ends up being used per flush, so perhaps it was added to reduce water consumption? What is this thing, and how does its presence affect my approach toward replacing the different pieces of the toilet?
I believe that you are correct and that the container was added to reduce the amount of water used per flush. As for whether it will affect your fix - it might. If the tank is leaking then unless it is cracked then there are only two places that it could be leaking from - where the inlet connects to the tank or where the tank connects to the bowl. If it's leaking from the inlet valve then the container would have no effect other than giving you less space to work. If it's leaking form the spud washer (the rubber gasket between the tank and bowl) then you may need to remove it to get to the bolts that hold the tank to the bowl (though it appears that the container has indentations that go around the bolt heads so again it may just come down to the only effect being a more cramped space to work).
I had a similar toilet that never flushed properly, resulting in multiple flushing and wasting water. I removed the tank, removed the flush valve and plastic dam, re-installed the flush valve and my toilet finally works properly.
To ensure it wasn't wasting water I measured 1.6 Gal of water, poured into the bowl, marked it, adjusted the fill rate just a little until the water in the bowl hits the mark every time.
No, I didn't use a permanent marker in my bowl - I used colored tape that stuck until I removed it.