Should dairy products be composted with other food waste?

I wouldn’t and don’t. Cheese, for example, will attract rodents. Compost should be vegetative matter.

I wouldn’t either. Milk would turn to Ammonia. Cheese will mould and break down, but it is rather nasty and wouldn’t add to mix well. Compost can include things like bones and meat, but your average backyard bin would just become a mess of maggots, so I don’t recommend it at all. You can include things like fingernail clippings and hair clippings.

Our compost waste is taken away by the local garbage service and it is treated at a specialised centre called Ecopro. http://ecopro.no/

http://www.mnn.com/lifestyle/recycling/stories/30-things-you-should-never-compost-or-recycle

If it’s going in your garden then no, definitely not. You can get special compost bins for cooked food that are sealed to prevent attracting vermin.

In my area though all waste is taken by the district council – we sort it into recycling, kitchen and garden waste (including cooked food), and general non-recyclable waste. It’s a good scheme. Could you campaign for your garbage service to include waste food including cooked? As @cazzie says the waste would need to be specially treated

About the only way I could see doing that would be just bury it in the ground and covering it with soil. It would probably take nitrogen out of the soil while it breaks down, so if it’s your garden watch the plant colors and supplement as needed.