What specs (lumens and contrast ratio) would you guess of a projector just by lookin at the image?

Question

if it could only operate well (not fading due to the light) in pitch black? and even starts to fade a bit from the dimmest of lights switched on in other rooms about 3.5 meters away but does not reflect so much that a shadow can exists on it.

Answer 1

less than  800 lumens but  it  depends on how the ratings  are done.  some  manufacturers  use  the  widest  possible  margin of  error to make  their  product specs  look  better  while  respectable  makers  use  very  tight  and  rigid  formulae to  give  a true  picture  of  what their  products  can do .  but you  have  to  know  all  the  variables and  how they inter-relate

Answer 2

You don't say how big the screen is, but I'd guess less than 200 lumens (and maybe much less since many projectors with measured brightnesses of 400-500 lumens can illuminate a 100" screen nicely in a dim room). As to contrat ratio there is no way to tell from your information.

You plainly have a projector with a very dim lamp. Either not a very capable projector or one in which the lamp is almost burnt out.