Battery levels will drop when connected to the charger - because of code in the battery controller. It's bad for the battery to stay at 100% for any amount of time, so the controller will cycle it in the 95-100% area. Smarter controllers will hide what they're doing.
Google chat messages can be delayed for any number of reasons, ranging from internal glitches to "Your network connectivity was bad at the precise moment the message was attempted to be delivered, thrice, and it retries at exponentially longer intervals."
But go from 5% to 0%? I am used to glitches but there are oddities here that are either hardware issues (battery discharging while low and connected to the charger), network issues. This is beyond what I am used to. Again, I could be connecting the dots incorrectly but I would not be surprised if I am right :-P
Google chat messages can be delayed for any number of reasons, ranging from internal glitches to "Your network connectivity was bad at the precise moment the message was attempted to be delivered, thrice, and it retries at exponentially longer intervals."