Click on "General" in the "Settings" section. Then make sure the "Reduce log output" is not selected. One the next Server Restart happens, you should be able to see the log file in the "Log Files" under the "Information" Section.
This will allow you to see a kill log?
Yes, kinda. If a player takes damage, it will show you their name, the time it happened, their coordinates on the map, current HP, damage taken, body part hit and the source of the damage. If a player is killed by another player, it will show the name of both players and the distance at which the kill occured.