The penny not only serves as a scale reference, but a DATE reference :)

Such an impressive stinger - let alone the distinctly flattened pygidial field - can only belong to a female. Therefore, this one insect was really the worst nightmare for several dozen of cicadas during her life (since Cicadas have nothing to fear from males).
Antennae are a good gender hallmark for Yellowjackets, and Vespids as a whole, true. But in Crabronid and Sphecid Wasps genders are far less easy to tell apart based on shape of antennae, especially on dead individuals who all tend to have "curled" antennae due to dessication. In fact, one often has to count every segment before being sure.

There's a park not far from here with sections of sandy ground. There are all kinds of burrows and Killers buzzing about the area. How many eggs is a female likely to lay? One egg to each burrow? How many cicadas per egg?

and two to three cicadas per female egg (usually only one for a male egg). Exact number of larval cells per burrow varies, some being used by more than one female. A very complete website especially dedicated to Sphecius speciosus exists. You'll find the link on the info-page of the Cicada-killer in BG.

I made a mistake, I apologise. I diddent realize how difficult it would be to tell them apart. I saw the stinger, but i had once heard that males of solitary species have a stinger.

nor venom glands. In some groups, including Cicada killer, spiny extensions of the last urosternite can sometimes be mistaken for a - small - stinger.