Measure times spent in run/sleep/deep sleep modes on STM32 boards

There isn't a way to do it at the moment - it wouldn't be ideal because you'd have to use the RTC which is only accurate to 1/32768th of a second, but I know what you mean - it's better than nothing.

Right now I'd say it's best to use setBusyIndicator/setSleepIndicator and an oscilloscope.

also give an idea of the eventuals problems of lost data when getting out of deep sleep mode.

What do you mean? Like issues waking up to respond to serial data?