Is there a way to see if the player already killed a rare/boss/etc and can't have any loot from it, using the mob ID/name?
Also is it possible to know the time remaining until it can be looted again?
I'm looking everywhere and couldn't find a way yet...
Rare loot lockout is usually tracked by hidden quest flags and is daily. Daily means it resets at US/EU coordinated reset time: http://wowreset.com
There is no API available to obtain the hidden quest flag for a kill. The only method to find the ID is to dump your completed quest IDs before the kill, then compare the dump to one after the kill. There should be one new ID. If you're not looking to be one of the first people to write an add-on, handynotes plugin, or weakaura for rares, just download another rare tracker and use the quest IDs they found.