There were reports of fires overheating while charging mobile phone batteries, similarly, could battery-powered cars, bikes, scooters, etc. catch fire or have there been any such accidents so far?
I am sharing as much as I can understand about this. First of all, not all batteries are equally dangerous. Some batteries are a little more risky. Which is a little less. Again, the battery is an alternative to the battery. So we have no choice but to make the use of batteries safer.
Mobile is a very small device.
This tiny but extremely powerful instrument is the result of the tireless work of engineers and expert designers. Like every electronic device, it is dependent on electricity. The problem is that it is not as big as other electronic devices. Moreover, portability or portability should be a major feature. So mobile companies include batteries with lots of power packs in a small space. Which makes the device a bit risky. Because, you see, you can't use very heavy protection on a small device.
Hopefully, the phone companies do a lot of tests before releasing any phone in the market. This is an important part of so many tests, how secure the phone is. So most of the time you are safe. I think the owner of the phone that caught fire is very unlucky. Many times it can also be due to the error of the phone company. For example, a special model of Samsung has been found to cause some fires due to design errors. Due to which they have to confiscate all the devices of that model. 
Photo source: Samsung Note 7 nightmare puts firm's brand on trial However, the risk factor is less as these devices are larger than the other batteries mentioned. However, I am not saying that it is completely risk free. Moreover, they are not as close to the body as the phone. So it can be said that it is much safer. Summary: Due to the small size of the mobile and the need for sufficient power, it is slightly more dangerous than the battery of other devices. However, none is above the risk! Everyone stay healthy and safe.