Hi N1kk1,
Welcome to the forum for Apple Support.
When a device is connected to WiFi, this doesn't necessarily mean that it has an active internet connection. It just means it's connected to the local network. It therefore could mean there is an issue within your home network. Rather than resetting your networking settings (which appears to make it work, likely because it's generating a new connection to your access point/router).
I would first try a reboot on your Router/Access Point and then seeing if this resolve the internet connection issue. I'm hopeful it should, if other devices are connecting successfully to the network and the internet.
As for the phone being on/off whilst on charge. There is no need to turn off the device whilst on charge - and in fact, it won't "charge quicker" as it's off. In fact, on the latest iOS and iPhones, the software will self-regulate the power it consumes to optimise the battery, such as a routine of charging.
It's actually recommended to keep your iPhone turned on, whilst charging - such as at night, as this can then install automatic updates, backup to iCloud, as well as learning the routing to optimise battery life/charging cycles.
I hope that this information has helped, or goes someway of helping.
