Microwave oven cabinet doesn't or shouldn't get hot though it is likely to if it is a combination microwave oven/grill being used for extended periods.
Assuming it isn't a combination type there is no more likelyhood of fire than if it was placed on any other surface.
A conventional microwave is quite heavy although the inverter type is much lighter and all the weight rests on just four points which over time could damage the surface.
Resting it on four substantial coasters would spread the load and minimise any long term damage to the surface...
No one can tell you without looking at it. You need to ask yourself how old is, what did you pay for item what does a new similar model cost, You can look at other brands = Ask yourself what do you cook in it, do you need all the features s and the size, Personally i would replace it.
Well....the first thing you need to check is see if you have power going to your RY9 relay. If you do, there is a good chance the relay is bad (if you haven't already) If you don't have power going to that relay, you have to trace where the power is being lost. Fuses is usually a go to. According to the schematic there is an inductor in line with the netural line, check that. As well as an inductor with the lead, and several fuses.
Make Sure the plastic ring with the wheels on it is underneath the turntable. Maybe the teeth of the turntable are not engaging fully with the teeth on the microwave. If not you could cut out some small 16th inch thick plastic sticky squares and put them on the high points of the teeth of either the microwave teeth or the turntable teeth. no metal Sticky pieces you know what happens one metal is in microwave .
Maybe the small motor underneath the microwave as loosened and has dropped down a little so that it is not engaging with the turn table fully.
Hope this helps.