Does CME have different contracts for different traders, i.e., some traders must close their positions before the last trading day of their futures contracts while others can hold their position to receive real crude oil? If so and I'm the former type of trader but does not close my position myself at the last day, at which price and at what time will CME close my position for me?
CME does offer financially-settled futures contracts for some commodities, which are settled based on the average price of the nearby physical futures contract. So if you don't want physical delivery then you can buy these contracts, but they are much less liquid (you may have a larger bid/ask spread to overcome).
I'm assuming your question is motivated by the recent negative oil price, so I would add that the futures contracts that went negative are all physically settled. Financially-settled contracts have not gone negative (and likely won't since they're based on an average price over a month). If you hold these contracts and don't want physical delivery then you must close them out prior to expiry.
If so and I'm the former type of trader but does not close my position myself at the last day, at which price and at what time will CME close my position for me?
They won't. Your broker may automatically sell to close your contract at some point, but it will likely be at the current bid price at that time.