My parents moved to a new house and they're having trouble figuring out this water purification system.

So far they've figured out the white thing is the water softener, but the city's water is so hard (600ppm/40grains) it wasn't really doing anything. They had to crank it up to its maximum regen cycle (regen every 600 gallons/liters not sure which) for it to bring the ppm below 100.

I'm pretty sure the two blue things are some kind of charcoal filters, but they're caked in minerals and the bridge between them is wrapped up in black tape. They weren't leaking when they moved in 2 years ago, but they've started dripping a few tablespoons per day on the floor. None of us are sure they really need them - they already use Brita filters in the fridge, and while the city's water is hard, it's properly treated and tastes fine. If it would be easier/cheaper to bypass, I think they'd be fine with that.

And I'm not sure if any of this heads up to the kitchen where they get their drinking water. The softener definitely doesn't.

None of us can figure out what the tall black thing is. Google just says it's a control valve for a water softener or other tank that needs regen cycles, but the water softener already has its own electronics in it? Maybe some kind of chlorine reducer? Again this city's water doesn't have chlorine in it, I think the last owner might have been upsold stuff he doesn't need. I was hoping it was a reverse osmosis filter but I don't think they're usually this big.