I'm going to be pedantic, but a shock absorber is the correct name for the spring, as it is that that absorbs the bumps on the road, and you are referring to the damper as this damps out the oscillations of the spring
Don't worry though I'm sure about 95% of the population don't name them correctly and I'm just being facetious
But unless a damper is gas pressurised, it will not return to the original position when compressed, only gas pressurised dampers do this.
And all dampers have oil if they are gas pressurised or not.
When the damper unit is removed unless you fit it on a damper dyno, there is no real way to tell how healthy it is unless there are obvious leaks from it.
When I had my Sachs dampers rebuilt for my Clio at BG Motorsport they actually build them and then match them on a damper dyno.
OEM dampers are only ever to within a tolerance of 10%, though recently Ford paid a lot extra to ensure there's were to within 5%, this is still no where near as accurate as the damper that Peugeot used to build inhouse around the time of the 306/406. It all went down hill when they started buying them in from outside suppliers!
OEM dampers are not much, you can buy Fiat, Monroe, Bilstein IIRC all do an OEM damper unit. The Monroe and Bilstein are gas pressured.
HTH