Are the popsicles in beating the eat time-limited?

Title say it all.

Yes, they are time limited unless they change the event (or break it or something).

What monsters would a level 200.. kill to get the quest items T_T..

Regardless of level, all monsters drop quest items, if I'm not mistaken.

For this particular quest, Gaga says you need to kill monsters no more than 11 levels below your own...

I got the items from some knight or other in stronghold (was in the mixed room). Not getting them now from random low-level mobs while hunting Eregos. make of that what you will.