All the current Kosher laws existed at the time of Christ and were enforced. Any pork products are trayf, unclean and are forbidden. Anything from the sea that has no scales is also trayf: lobster, shrimp, carp. The intent is to eat no bottom feeders, since the rabbis noticed that fish have an inadequate waste disposal system. Any dish that combines a dairy product with a meat product is forbidden. The Baalites' favorite feast day dish was a calf cooked in its mother's milk, and that was seen as an insult God's creation and motherhood. Cheeseburgers are trayf. Strict Orthodox homes have two stoves, two refrigerators, two sets of pots and pans and cutlery so that not a single atom of cheese or milk can infect any meat dish, or vice versa.
Dairy can be mixed with dish and chicken.
Salad dressing has no dairy in it. It would be trayf to put mayo (which has dairy in it) on any sort of beef, mutton or goat.