During KYOcount configuration I press the test button to check the mail server, the result is negative. I double checked the mail server address with the administrator and it’s correct. Can I still use this mail server?

When using the test button the mail server is tested by using ip commands, if the firewall doesn’t allow these commands to the mail server for security reasons, the test will be negative. But emailing will/can still be successful, as ip commands used to test a connection are different from commands using email. The firewall can distinguish between those commands and will still allow email traffic.