To get one thing out of the way, there is not a single case of a microwave-oven having caused cancer on its own. Ever. It's just not how microwaves work. At the frequency that the electromagnetic waves are emitted by the ovens, it's not possible for it to cause cancer even if the unit were defective and leaking. Furthermore, there are no lingering microwaves or radiation on the food (well, apart from what was already there) that could cause cancer because, again, that's just not how microwaves work.
This is a myth that has been perpetuated for decades that has no basis in reality (likely because some scientist made the mistake of saying it operated using "micro-wave radiation" in public during the time when everyone was paranoid of nuclear war). The worst thing that can happen is you can get a severe burn if you were directly exposed to the microwaves for too long (which you would definitely notice).
Now, as far as the plate is concerned, I'm assuming that this plate is one of these Signoraware plates on Amazon. The description says they are made of polypropylene (confirmed by the recycling ID code 5 on the plate), which is said to be microwave-safe at temperatures up to 250 °C before warping. It's possible that the steam formed from surface water trapped under the vermicelli in contact with the plate super-heated to those temperatures which caused the warping.
From this point, I'm going to separate my answer into the objective and subjective sections as I'm having troubles finding any definitive answer one way or the other:
Objectively, there is likely nothing wrong with the plate - it's just a bit disfigured. The only real danger is that, if it continues to warp multiple times, it can become brittle leading to surface cracks and, ultimately, breakage. But for the time being, as long as the warping doesn't bother you too much, you can just keep using the plate as normal. In the future you should create a well in the center of the food you are reheating so as to limit how much heat can build up in one place, and that should help keep this from happening again.
Subjectively (and take this with a grain of salt because, again, I cannot find a definitive answer on this from a reputable source), I would throw it out. When plastic warps, it's often a sign that it has begun to break down, and from that point on it can leech into whatever food it comes in contact with. I have no idea if polypropylene follows this trend and to what degree, but a recent study has found that it has a tendency to leech microplastics into warm/hot beverages, so I imagine the problem is exacerbated when the polypropylene has been heated to the point that it has begun warping. I'm not sure I would trust the plate any more than I would trust a Teflon non-stick pan that's been destroyed by the frequent use of metal utensils over time.