Would you still go to the Internet via WLAN during thunderstorms?
Yeah, why not?
Yes, I always do that if there's no power failure.
Did I skip something now?
Why should not I go to the internet via my mobile phone / laptop via WLAN?
wireless means wireless. What should a flash do?
The flash will not reach the Wi-Fi in your laptop.
About the power adapter?
If your router is not nice and expensive you can try it…
It's impossible for a simple flash to go through the entire power network of your house and then reach your power supply and overload it. The only thing that could happen would be power outages in your area during heavy storms, which can (but do not have to) hurt a PC if it is unexpectedly disconnected from the power supply. However, since you have a laptop you will not have to worry about a sudden shutdown unless you tear out the battery.