Can I get a work card, social security number and medical insurance without a green card after marriage?

Of course. A green card, that is, a permanent residence permit for foreigners, is a permanent residence permit for foreign citizens. As long as they meet the legal status of buying insurance on the medical insurance website, they can buy their own work card, social insurance number and medical insurance, but they can't enjoy low-income free medical care without a green card. Holding a green card means that the cardholder has the permanent residence in the issuing country, and at the same time, holding a green card can exempt entry visas for a certain period of time.