I don't really use my 4540s that much (should sell it), but I have not noticed the issues you mention.
If you want to provide clear/detailed/step-by-step reproduce steps, I will attempt the same thing here.
Now, it shutted down around 10 %, didn't turn on blinking light, plugged AC in, booted to macOS showed 0 % unplugged the AC jumps to 20 %.
1. Fully charge the ProBook
2. Go to System Information and take a look at the Full Charge capacity. Note the value
3. Unplug the AC, refresh via Command + R, take a look again at Full Charge capacity and it changes. (First thing)
4. Let it die until it turns off (note the battery % at which it turns off)
5. Now, you can't turn it on because of the dead battery.
6. Plug the AC in, turn on the ProBook, and now the battery shows 0 %
7. Unplug the AC and now the battery % should be more, like 15-20 % and also, the Full Charge capacity should be different in System information.
The thing is that I am not sure at all if it's my battery or is just the kext or ACPI which is acting crazy.