Ok, you're putting yourself and your friend in deadly danger.
First of all, your 29$ device is not a substitute for proper RF qualification. It simply isn't. You might be able to find a concentrated leak in the expected frequency range with that, but all you said is that you tweaked around with the magnetron, probably replaced it, and might have to deal with different frequencies now. All in all, you're also putting your health in the hands of a device without any specs on sensitivity whatsoever. I hope you don't do that with medicine, cars, building material… or else, people will die. This device is snake oil, nothing more. So, whilst I strongly recommend you do not take it displaying "everything's OK" as an OK for things being actually OK, it displaying "danger" might be a good indication to quickly back up, turn off the microwave (eg by opening the circuit breaker), unplugging it, and putting it on the trash, where it belongs as a device that can, literally, fry your brains or cook your gonads.
Then, magnetrons are dangerous, as they contain very poisonous elements that they expose when broken. Please dispose of the broken Magnetron carefully.
Also note that microwave ovens have high-voltage generators inside. It's not very likely, but your modification might lead to those generating discharge that leads X-Ray irradiation. Please be careful.
You're clearly not qualified for this kind of work, so please avoid harming yourself and others. I know this sounds harsh, but right now I'm mostly worried about your and your friend's health.
These holes were put in by the manufacturer.
I was wondering, should I patch these holes?
How on earth do you think that's a good idea. If your microwave is leaking radiation, then surely not through the holes the manufacturer made, but through some defect (corrosion? your unqualified labor?) or other effect. Plugging holes that you think are for thermal regulation will, at the very best, lead to a fire hazard.
Seriously, leave the microwave alone.