Evaluating likelihood of egg breaking when falling in random container on concrete
This question might be better answered on the physics stackexchange, but I'll take a crack at it.

Although the factors you mentioned probably affect the likelihood the egg will break, some of them are not specific enough to be descriptive features. For example, how do you quantify "shape"? I will try to provide some more features that can be quantified, but some of them might take effort to retrieve.



Egg Features


Eggshell thickness


the thickness will probably not be constant, so you can take the mean, standard deviation, and even isolate some key points on the egg to sample such as the top/bottom points.
some studies indicate that "eggs with thin but more uniform eggshell were stronger than those with thick but less uniform eggshell" from this paper
you might be able to measure thickness using optical techniques such as imaging or lasers.

Temperature


both of the egg and the surroundings

Time since egg was laid


this might be approximated by the expiration date, particularly when only using a single brand

Density


you can calculate this by putting the egg in water (fresh eggs sink) to first determine the volume, then divide the mass by this volume.

Calcium deposits


the bumps you can see and sometimes feel on chicken eggs are calcium deposits that range in frequency and size. I am not sure how you would quantify these, but they could be another factor.



Wikipedia indicates some abnormalities with eggs that you might want to account for or remove from your samples. I copied the abnormalities here:


double-yolk eggs
yolkless eggs
Double-shelled eggs: where an egg may have two or more outer shells, is caused by a counter-peristalsis contraction and occurs when a second oocyte is released by the ovary before the first egg has completely traveled through the oviduct and been laid.
Shell-less or thin-shell eggs possibly caused by egg drop syndrome




Container Features

ideally the impact energy would not be absorbed by the egg, so somehow you need to measure this using estimates of the material metrics as well as shape parameters. One such measurement might be:


Average surface area that contacts the ground


You might find looking at the container's convex hull useful for visualization purposes



Many other factors can contribute such as:


Hardness
Resilience
Elasticity
Stiffness
Ductility




Lastly, there are probably many features that can be calculated by combining the egg and container, but those seem to be much more complicated. For example, measuring the amount of movement, on average, an egg can endure within a container by applying pressure to certain areas. I am not sure how you would easily extract these types of data, but they certainly exist.