What kind of cookware can melt in a microwave? Is it safe to eat food cooked in a melted cookware?
The cause is that the dish was not intended for use in convection mode. 

Plastic melts under heat, period. "Convection" as used by oven manufacturers means that the air in the oven gets heated to the temperature specified (actually, ovens are so badly calibrated that it can be considerably more - I have seen an oven overheating by 40°C - so a considerable safety margin is needed). Any solid objects heat to high temperatures in this hot air, with the surface coming close to the air temperature. You cannot put plastic in a 180°C oven. 

A microwave oven operates on a different principle. It heats certain types of objects from inside. Water (and some other nutrients, e.g. fats) get hot when irradiated by microwaves. Plastic or air don't get hot. Therefore, a plastic dish does not get hot when used for cooking in a microwave oven, and the air in the oven also stays cool and does not melt the dish. 

What you have is actually two ovens in one. They use the same heating container, but with two different heaters. The plastic dishes supplied with the oven, as well as any other specialized microwave cooking dishes, can only be used in microwave mode. The convection has to be turned off when you use them, else they will melt. 

If you want to cook with convection, you have to use a pan from a material which doesn't melt. For a traditional oven, this would be borosilicate glass, ceramic, silicone or metal. I would not use a metal pan. I have heard of combo ovens which don't turn off the microwave part when switched to convection mode (even if the user manual claims otherwise!), and even if yours does, it is still a safety risk because you might forget it and turn on the wrong mode. Metal gets much hotter than water in a microwave, up to the point where it can explode. 

Summary: use oven-safe glass, or ceramic. If your glass dish has a plastic lid, remove it before baking in convection mode.