Can I estimate remaining battery life by measuring its voltage with the same MCU that it powers?
You can do this (assuming voltage is a predictable function of remaining life, but that's another issue) as long as there is a fixed voltage reference available in the system somewhere.  Some micros have a fixed voltage reference built in, which can usually be read by the internal A/D or applied as the A/D scale.  If not, you have to supply some external reference.  Note that due to power consumption you may want the micro to switch on this reference only for a short time around battery readings, which don't need be very often relative to the time it takes to do a reading.