Can they? Sure.
Anything is possible.
A physicist walks into a bar, goes up to the counter, and orders two drinks. He drinks one himself, and places the other one on the bar in front of the empty stool next to him. When the bartender asks him who it's for, he says "well the uncertainty principle says that it's possible, however unlikely, that all the atoms in the vicinity of that stool might spontaneously rearrange themselves into a beautiful woman, and if that happens, I'd like to be able to offer her this drink." The bartender says "well there are plenty of beautiful women in the bar already, why don't you just try offering it to one of them? You never know, she just might accept." To which the physicist responds "yeah, right, what are the chances of that happening?"
Will they? Not likely. Most of the battery incidents you hear about are caused by people short-circuiting a battery cell, either by carrying loose cells in their pocket, or by using a "pinless" or "hybrid-style" mechanical mod with an incompatible atomizer attachment. Something like your EVOD battery is more than just a cell, it also has the button, the housing, the connection, and the circuitry all built-in to one unit, and if it detects a short-circuit (or indeed, any resistance that's outside of the "safe" range will be considered a "short"), then it simply won't fire.
As for charging, just make sure you use the charger that came with it, and you should be in good shape. If you use it with a different kind of charger, then there's a chance that it could have reversed polarity (+ where the - should be, and vice versa) and that could also lead to a catastrophic failure. "Most" pen-style vapes, and their chargers, are standardized to use the same polarity these days, but it's always better to be safe than sorry, so just always use the one that came with it, and there shouldn't be any problem.