I was cooking some food when I noticed a burning plastic smell and some smoke coming out of the knob, I let it cool down, and when I turned it back on, there wasn't any smoke but the burning smell returned, is the plate damaged, or is it some stuck food being burned?
The burning plastic smell seems to be coming from the plate, even when it is dissassembled like this, i can smell it from the centre.
I feel like the other side of that central plate has your answer. Pop the central screw and see what is on the other side of that discoloration.
Looks the same on the other side, the pattern on the unburnt metal looks like galvanized steel, did the zinc burn off?
That looks like it, maybe use vinegar to dissolve the zinc?