Which scale inhibitor should you actually buy for a tankless water heater?

No. A scale inhibitor sequesters hardness minerals in solution so they do not deposit as scale inside a heat exchanger, and it does not remove them. A hardness test taken anywhere else in the house, before or after the protected line rejoins the rest of the plumbing, reads exactly the same number. Only a water softener changes a measured hardness reading, since it actually exchanges the minerals out.

No. A scale inhibitor slows how fast scale forms and does not eliminate it, and it does nothing about deposits already present before installation. Most manufacturers publish an annual flush interval in their own service documentation regardless of what protection is installed upstream, and skipping it on hard water is a common way to void a tankless warranty even with an inhibitor in place.

The polyphosphate cartridges sold for this purpose are food grade compounds dosed in small concentrations, and manufacturers publish that specification on the listing itself. This is a separate question from whether polyphosphate addresses anything else in the water. A scale inhibitor does nothing about bacteria, nitrate, lead, arsenic or PFAS, and none of those is a do it yourself topic regardless of what treatment is installed for scale.

Generally no. A whole house softener removes hardness minerals from every fixture, including the line feeding a tankless heater, so an additional point of use scale inhibitor is protecting against a problem the softener has already solved. A scale inhibitor earns its place specifically where a full softener is not installed, such as a floor drain restriction, an HOA rule, a rental unit, or a household that measured its hardness and chose not to soften.

It depends on the unit and on measured hardness, since a higher grain reading uses the cartridge faster. A budget T fitting system is commonly rated around six months of typical use, while the reference branded unit's replacement interval is published on its own listing. Check your measured hardness against the manufacturer's stated service life rather than assuming a fixed number applies to every household.

There is no single published threshold, since manufacturers vary in what they assume. As a general guide from the trade rather than a regulatory limit, anything in the moderately hard range and above, roughly 7 grains per gallon or 120 mg/L, is commonly treated as worth protecting against on a tankless unit, given how much faster its heat exchanger scales compared to a standard tank heater.