Actually, the issue here seems fairly clear in looking at your troubleshooting... discounting the fact that your router is 9 years old and likely not up to current standards, you did state:
I don't think the problem is my Wi-Fi Router(D-Link DIR-600M) because the issue occurs with WiFi Routers at my workplace, Friend's home as well.
Considering you have tried this on multiple networks and connections, and you have factory reset and performed a network reset multiple times, the conclusion can only be that your phone is defective. You should contact Moto for a warranty replacement, or just consider replacing it if it is no longer under warranty.
In looking at all the troubleshooting you have done, and given the above quoted statement you made there doesn't seem to be any other possible cause.
There is no known issue with WiFi on the Moto G5+ in any Android version or release, and since this is not related to a single router or connection, the issue seems quite clear, your Moto is defective.