Yes Maurice, more sophisticated products as you say, like my own digital camera and power tools etc etc, do indicate when fully charged.
Even relatively inexpensive items such as my vape batteries also have an LCD display which indicates when the batteries are fully charged.
There are however, many other devices made now that simply supply you only with a USB lead for them which as you say, can connect to your computer or car USB or cigarette lighter port etc etc, that have no indication of their remaining power level.
I don't think you can ever do it any harm to it charging it overnight but my advice would be to charge it during your waking hours from your pc if it makes you feel safer in your home.
Some unscrupulous counterfeit devices deriving from China, have been known to set on fire due to poor manufacturing standards and cheap components used in them without the necessary safety devices also fitted.
Even some fairly expensive ones like a certain range of Samsung phones I can instantly think of have also suffered from potentially hazardous power supplies to the units so I'd say, unless you are entirely certain it is manufactured to European safety standards and regulations, I'd err on the side of caution and perhaps charge it during the daytime where you can your eye on it, certainly until your confidence is sufficiently earned at any rate.