Which element is cheapest by mass?

Chlorine, sulfur and carbon (as coal) are cheapest by mass. Hydrogen, nitrogen, oxygen and chlorine are cheapest by volume at atmospheric pressure. When there is no public data on the element in its pure form, price of a compound is used, per mass of element contained.

Which element is the most expensive?

Lutetium is the most expensive element that you could actually order and purchase. The price for 100 grams of lutetium is around $10,000. So, from a practical standpoint, lutetium is the most expensive element. The transuranium elements, in general, are extremely expensive.

Why are superheavy elements so expensive?

For example, the superheavy elements at the end of the periodic table are so unstable that even the researchers studying them typically don't have a sample for more than a fraction of a second. The cost of these elements is essentially the price tag of their synthesis, which runs into millions or billions of dollars per atom.