Eggshells may break down but they never fully decompose. And this has been substantiated by scientific trials. By 'breaking down', I mean that any physical activity that involves the egg shells breaks them into smaller and smaller pieces so no obvious visible evidence that the shells remain. That includes adding to the compost (where even the weight of other ingredients can shatter them, let alone turning, etc.) or activities of soil organisms and plant roots exerting pressures. A reasonable assumption to conclude that because they can no longer be seen or recognized as egg shells they have decomposed but those individual shell pieces - regardless of size - will remain intact indefinitely. There are actually archeological digs that have found evidence of egg shells that are more than a 100 years old. And still almost fully intact.

"Apparently they are attracted to beer. If you bury a container up to the edge that has some beer at the bottom, they will crawl in and stay until they drown. Since they are all in your compost pile as of now, this might do the trick for you." I read somewhere that it's actually the yeast in the beer that attracts them. According to that article (sorry, no link, going from memory) if you reconstitute some yeast in water and add some sugar (or honey, syrup, etc) you can get the same results.

Roaches are part of nature's cleanup crew, which is why we don't put the compost bin right next to the patio door. The ones I see (in central MO) are 'wood roaches' rather than the German cockroaches that you see more often indoors and are considered a household pest. Not that these never come inside. As for heat, compost is not heated by the sun but by microbial action. If you aren't filling the entire bin with a fresh balanced mix of ingredients all at once, it probably won't heat up, but you'll get compost anyway.

I have an interesting guest in my cp. I have alot of frogs in the yard, the other day I noticed a large one right on top in the middle of the burlap sack that covers my pile. I moved him to add some scraps. Last night several friends had come to join him.