First and most importantly, you and your family are safe - and major damage to you or your home has fortunately been averted.
Clearly, you are concerned. Quite understandably, you and others would be worried after such an experience. Nothing can be said here that will remove that concern, but hopefully you may take some reassurance that your experience is not common. As for statistics as catastrophic battery failures for iPad, I’m not aware of published information in this regard.
Due to the rarity of Li-ion battery failures of this nature, they tend to receive a lot lot of attention when they do occur. Recent examples of battery fires associated with electric vehicles (such as Tesla) are testament. Some years ago, Samsung mobile phones experienced negative publicity for similar battery “events” - one, at least, occurring on-board a commercial airline while in flight. It follows that the bigger the battery, the more electrical energy is involved, with larger potential consequence.
Li-ion battery failures can and do occur - but the relative occurrence within the millions (billions?) of devices that are in regular use is/are thankfully rare. The phenomenon of battery failure is not specific to any single device or manufacturer - but can affect any device that includes a power source or rechargeable battery, Li-ion batteries being no exception.
Clearly the failed device, an iPad is this instance, requires expert examination to establish the possible cause.
Your battery operated devices, including your Apple devices, should be entirely safe to use and charge per the manufacturers instructions. For Apple devices, they are designed to be left connected to their Power Adapter for extended periods - charging being automatically regulated by the device and its connected Power Adapter. As with any electrically powered device or appliance, leaving it unnecessarily connected to AC-power always carries risk - but for healthy/undamaged equipment the attendant risk is minimal.
Whether or not you choose to charge devices overnight or when not present is largely a matter of personal choice.
Having made you report of the failure to Apple Support - and in returning your iPad for examination - I sincerely hope (and have little doubt) that you will receive an appropriate report in due course.
In the meantime, insofar as I can, I do hope that you will be reassured as to the rarity of this event. If other members of the ASC Community have comments to offer, they will surely do so.
