Hello. For the Elite 200 v2, is it okay to charge the power station while it is charging other electronic devices?
Or should everything be disconnected from the power station while it charges itself?
Short answer - Yes.
The V2 has pass through charging. This means that if your load is less than the charge rate, the load is using grid power and the balance is charging the V2 at the same time. If your load is higher than charge rate i.e. maximum output, it runs from grid and may even use some battery to get to 2600W.
The obvious aim is to keep the load less than grid input so some charge is given to the battery. 
What about charging overnight. I.e. just like a phone or tablet or other electronic device. Is it bad to leave the elite 200 v2 plugged in all night after it reaches 100% and stays that way until morning when it is unplugged?
or just unplug it right away when it reaches 100%?
@sacrilegious It is fine to leave the AC200L on charge overnight. When it is full it will stop charging. The other thing to consider is UPS. I do this when away from home with an AC70 & a couple of AC180s (same applies for the 200L). I plug my AC70 into grid power an the WiFi router fibre boxes into the AC70, with the grid switched on.
Once the AC70 is full it has what is called pass through supply i.e. the devices are powered from the grid through the AC70. If the grid goes down, the AC70 inverter kicks in without missing a beat. It will continue to power those devices until one of 2 things happen… 1. The AC70 battery goes flat, or, 2. the grid comes back on. If the grid comes on, it supplies power to the loads plugged into the AC70 &, if there is enough residual current, the surplus recharges the AC70 battery.
No, its not bad, it’s designed to do exactly that. I should note, phone batteries are a different lithium chemistry to the LiFePO4 of Bluetti power banks and far far safer. The Bluetti battery management system stops over charging amongst other things.