Warning: high resolution photos (you can zoom in really close up):
They dont look like the roach eggs i've seen online...
The place I am renting here in Michigan has both a roach and rodent problem, unfortunately, and obviously I was not aware of this before signing the lease. what you see in the photos next to the "hatched eggs" (?) are 2 rodent traps. (I have no idea what they are, and no idea what to call them really)
The area where the photo was taken - where the traps are, and where the "eggs" are - is in an area where I have seen a rodent on 2 separate occasions. Bigger than a field mouse, rounder, a medium brown color or perhaps a little darker. I'd say the one I saw was probably the size of a baseball, or a shade smaller.
(Regarding the caulking: There was a significant gap between the wall and the flooring, I assume that's where the rodents were getting in and out. The last guy the landlord sent over filled it in with caulking)