I tried all of your solutions with the same results.  Pre-water softner spots with both iron and calcium.  post softner just has calcium.  And I can't dry the windows without streaks no matter which type of drying method I use.  My solution is to go to a car wash.  They blow dry it while still wet.  Cleans much better than I can.  Costs $10.  Worth it to me

Nos681 wrote:

Is it a portable water softener that uses salt?

Or perhaps a media used to remove iron in hard water.

The second stage is probably carbon filter.

All guesses from appearance in video.

I have a shallow well and have iron just barely enough to taste depending on the season.

The iron separator has a media (looks like pebbles).

Did not care to have the water softened by salt…besides the fact it is suggested to not drink softened water…my understanding of process.

Water conditioned with a brine tank system is perfectly safe to drink.  The brine is merely used to backwash the filter media; it doesn't end up in the water you drink.  I've lived in the same house with the same water conditioning system my entire life.  If you have well water the exact nature of the conditioning will depend on the location.  I don't have hard water that needs to be softened; my water is already soft.  So my conditioner is really just to remove iron.  If the settings on the system are wrong you can end up with a salt taste after treatment, but that can be alleviated by simply running the water for a couple minutes, as its just indicative that there's still brine left in the filter media (too high a salt setting).  Typically you set the system to backwash at a time when no one is using water, as the conditioner is bypassed as the media is cleaned.  Mine is set for 2AM.  I also have a charcoal filter on my kitchen sink cold line because that's the faucet we typically use for drinking water.  I change that filter every 6 months.  Its really just overkill.  If the conditioner is set right and working all the water in the house seems to be the same.  Now, my outdoor hose bibs do not put out conditioned water, so the car washing thing is something I've thought about, because if I don't dry a dark vehicle it does get water spots. 
 

The last time I used water on my car war 2014, after a grimy three day drive home from Savannah.
I do the same as RPM, quick detailer regularly and clay bar once a year.