1) absolutely not. Like any good smartphone or laptop, the charge control circuit automatically stops feeing a charging current into the batteries for the earbuds and the charging case the moment the charge control detects the batteries are 100% full. Now, for long-term storage, it's recommended to keep lithium batteries between 50 and 80%, but this would be for a period of over 6 months.
2) from what I can tell, these earbuds use the same standard profiles that any Bluetooth stereo headset would use. You should be fine, but if your current sound subsystem gives you issues with lag or stutter, you can always try another sound library.