But my ISP is located in my city, you are showing a different city

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The source for IP address data is the regional internet registries which allocate and distribute IP addresses amongst organizations located in their respective service regions, like ARIN in America, if your ISP location is incorrect it mean they do not provide accurate data to their IP registry or data is not updated yet
Do not ISPs use NAT? As far as I know it is not possible to use the same public IP at the same time, is it?
I do not understand, but they use same IP for multiple users at same time and it's completely possible, like VPN services or even your home router