here the answers:
1) probably, even if you deleted the Manager, the IP address of the gateway is still saved into the syslog configuration.
Probably the gateway is still on and it's keep on sending logs. That's why you are still seeing the log file. To solve this you have to:
1) turn the gateway off;
2) edit/create a gateway, set the IP address of the deleted gateway in the "Internet Connection IP Address or DynDNS Name" field and save the configuration.
3) remove the IP address set at point 2 and save configuration again.
System should also deletes the IP from the syslog configuration. So I've already alerted developers in order to check this.
2) System writes all the daily log in the userlog-GatewayR****.log file. At 23:59:59 system makes a zip of that log and creates the userlog-GatewayR****-20171125-235959. Then the userlog-GatewayR****.log file starts to write the log of the new day and so on.
3) userslog-20171125-235959.log file would be the entire users' log. Having log's file with the gateway name it means that you set that users' log file to be written into a single file for every gateway. In this way system generates the userslog-20171125-235959.log file as well but it's blank.