To the engineers in this group, with a car with say 20% of its capacity lost, will it cost a full 100% to charge 80% of the battery, or there is no loss in eletrons? In dollars, a 100kW battery charge costs 12U$ at 12c/kW. When the battery looses its capacity to 80%, will it cost ~U$10 or $12 to fill it up? Thanks.

Are you paying per minute or per kW? That determines your answer. Upon re-reading your question, you appear to be asking if 80% capacity means 20% lost every time you charge. Answer: no. 80% capacity is just max storage. It is roughly analogous to a bucket that gets a little sediment every time it is filled, so eventually you have a bunch of sediment and can't put as much in the bucket.

You will lose electricity in terms of charge efficiency and losses from transmission, etc. So 100kwh out isn't 100kwh into the battery. A rough estimate is 10% charging losses.

Got it, thank you all! My wrong analogy was to a blender that keeps moving irrespective of demand, and that one would pay a fixed amount irrespective of outcome.

The proper units here for battery capacity and price from the utility are kWh, NOT "kW". There are a few utilities w/residential plans where they not only bill per kWh but also have demand charges, but that's rare and complicates calculations. (Demand charges aren't unusual on many commercial plans.) Charging rate would be measured in kW.