Anything that used to be alive is compostable. Different things take different lengths of time to compost, that's all -- and some things attract vermin.

General composting advice is not to use cooked food or meat, since it attracts vermin. I would probably put used vegetable oil in my compost, but I would avoid lard or meat fat.

As recently as the 1980s, you would very occasionally find an egg containing a foetus in a shop-bought box. Producers check by holding the egg to a bright light. Nowadays that process is automated.

Wouldn't it be more reliable to ask at the restaurant? I'd love to hear their answer.

Until it's the strength you like. There is no better answer. Surely nobody drinks tea for a caffeine buzz?

I'm not sure about this because (a) cooked = temperature plus time, and this hasn't measured time, and (b) the necessary temperature (and time) will depend on the variety of potato. Whereas testing the actual desired properties of the potato (softness) is direct.

@Aaronut B. Cereus infection is more to do with leaving cooked rice at room temperature for hours.

No, it's heat that's cooking it - and contact with water that's hydrating it. Unless you use a pressure cooker, it won't get hotter than 100°C. Bubbling is just a waste of heat.

Rice retailed in the developed world is not "dried-on-the-side-of-the-highway dirty". It would be illegal to sell it in such a state.