Yes, curved lenses, same curve on front and back .... Or flat lenses with same curve on front and back are called plano lenses.
So all "non RX" lenses, without power are considered plano lenses. This is widely accepted industry standard.
In glasses a "plano-convex" lens would be called a "plus" lens. This magnifiers and has plus power... The plus power would be measured in diopters. So if front curve is 8.75 D, and back is flat (0 D). The total power of that "Plano convex" lens is +8.75 sphere.
It would have a focal length = 1/D of only 11 cm, or about 4.5 inches. I hope that helps....
OK, but then the "industry standard" deviate from the optics definition used in other places where "plano" means that the lens has (one) flat surface. I'm not testing you, just curious why/if glasses use different nomenclature than photo optics, which wouldn't be too surprising.
A miniscus lens, without power, per your definition is a plano lens. Not "Plano" curved, but "Plano" power. See Plano curve means 0 base curve. Plano power means the front and back surfaced are parallel.
No, not per my definition! I'd call it a meniscus when both surfaces are facing the same way and none of them are plane.
Never heard of "plano power", but I'm sure you know that better than me.