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All these foods are technically allowed on a Primal plan.
Milk and honey are suggested to be limited since they are somewhat high in carbs. Mark has eased his stance on carb restriction somewhat over the years since the book was written. He also recommends lower carb, higher fat forms of dairy in general.
Storebought mayonnaise is not recommended because it almost always has a vegetable oil (canola/soybean) as the primary ingredient. If you make your own mayonnaise at home using a healthy fat, it is fine.
Here are some posts to clarify:
The Definitive Guide to Dairy | Mark's Daily Apple
Homemade Ghee Mayo | Mark's Daily Apple