First, I'm not a pro...
Sounds like you have a bunch of sediment in the lines. THis could have damaged the pump and or valves on the dishwasher and could very well have clogged the screens in the faucets and showerhead. I'd remove each of the screens in the faucets and showerheads and clean them. My guess is thatyou'll see a bunch of sediment in them. As to the large tank, my guess is thatit is a water softener. If so, and your water is hard, it probably ran out of salt. You should be able to find a name and maybe a model number on it, and then look up info from the manufacturer on the web. It requires periodic maintenance.
Is the filter that was installed a sediment filter? or a carbon activated one for taste? While flushing things out, you probably got a bunch of sand, etc. forced into the lines and that is what is causing you your current problems.
Note, if you have a bunch of sand in the screens of the faucets and showerheads, then you'll probably have similar problems with the toilet valves, as well. Many of the moden flush valves are easily disassembled and you can clean them out as well.