It's a genuine ID plate and presumably engine but there are a number of other numbers and codes to check on the body shell to make sure it's a genuine shell. Do a search for Cooper 'S' on this site as I put a lot of info on identifying genuine shells in reply to a post a few weeks ago. You need to check body numbers and production codes etc. The fact that the ID plate is NOT fixed to the bodyshell is not necessarily a bad thing but it's not a good idea to remove it to repaint the shell and must bring into question the originality of the shell. (IMO anyway). There are plenty of fake cars around and just having an ID plate and a shell doesn't make it genuine. From the photo it is missing the vertical grille panel brace and the oil cooler is not on the engine. An early body shell should have the first type floor pan without the full length protection plates covering the hydro pipes etc. This didn't appear till 67. The CAR number range quoted are for cars built up to early/ mid 66. My first S was CAR No 1090 and was in this range and was purchased in July 66. It should have four protection plates, 2 at each end corner of the centre tunnel. It would originally have had rubber inner Unis. Check that the CAR number (without YKG2S2 prefix) is stamped on the shell immediately below where the ID plate should be fixed. Check the BODY number is approx 500 less than the CAR number and the production code is
M2
06
and they should both be stamped on the top of the radiator shroud panel.
This should give you a good idea of whether the shell is genuine. As for price etc - absolutely no idea.
Regards
RonR