League-of-legends – Does exhaustaffect Karthus damage while he is undead

No. Minions have nothing to do with the champions stats or effects unless they are minions created by the champions abilities (excluding Malzahars pet voidling) such as Yorick ghouls which scale off his attack damage and max hp, Shaco clone which is given statistics from the original Shaco and Mordekaisers Pet of the grave which is given stats from Mordekaiser. Those are the few champions which are the exception to the rule.

Hope this was helpful.

Requiem channels for 3 seconds, which gives 4 seconds of actual time to Lay Waste. Lay waste has a base cooldown of 1 second. Lay waste also explodes after .5 seconds (though karthus can cast other abilities while it's waiting to explode)

At a CDR of 0

With immediate reaction time, 4 lay wastes are possible, since each will have a 1 second cooldown. Immediate reaction time is not feasible, though, so let's call it 3 Lay wastes

At a CDR of 40

Lay waste's cooldown becomes .6 seconds. Meaning Karthus can get of 6 Lay Wastes in 3.6 seconds. This assumes, however, that there is no more than .4 seconds of total delay between Lay Waste coming off cooldown and being cast again. This is likely difficult, but theoretically possible.