Check whether an IMEI number has a valid format using the Luhn check, and see its parts.
This checks the number's format with the Luhn formula. It doesn't prove the phone is genuine or not blacklisted — use your country's official CEIR/KYM service for that.
Dial *#06# on your phone or look in Settings > About phone.
No. It checks the number's format only.
No. Everything is worked out in your browser and nothing you type is sent to a server.