DoD means Day of Departure
I have never heard about this “CS class”. But I am not an expert of KVS.
O inventory may appear at any time to upgrade with miles so I recommend you to check at least on a daily basis.
For paid upgrade at OLCI/DoD
, the offers are indeed targeted (and customized price-wise). But, even if you are not targeted, you can ask at the airport at a customer service desk.