Squash, melons, and cukes often abort small fruit, sometimes before the flower has opened. It can result from high temps, inadequate water, or the plant's inability to support more fruit, among other causes.
If the fruit fails after the flower dies, another possible reason is incomplete pollination. You can pollinate them yourself by picking a male flower and rubbing the relevant parts on the relevant parts of a female flower. Be sure to do this no later than mid-morning.
Another possibility might be blossom-end rot (it affects more than just tomatoes).
Missouri Botanical Garden's page on blossom-end rot in cucurbits
I have no idea about the fruit shape issue. [Are you sure the two shapes don't come from different vines? I have a tomato situation like that: fruit of two different shapes and colors on what I thought was a single, multi-stemmed vine but must be two different plants growing together. The black beefsteaks are the labelled variety; the smaller dark pink oblongs with the wonderful taste are something else, probably a cross.]
If you don't get an answer here, you could ask at GardenWeb's Veggie or Squash forums (you must be a member to post, but membership is free):
Vegetable forum
Pumpkins, squash, and gourds forum
My zucchinni have done the same thing!
Too many disasters to list this hot summer in eastern New Mexico...no spring, just super hot for weeks, and no rain.
Three zuke plants came up together. I know they are heirloom seeds, but I don’t know the type. The leaves are pale green. They put out zukes in abundance, but they were all stunted, and rotted. I got some small round ones like yours. Two of the plants died.
I have a standard zuke with dark leaves doing just fine.
My raised garden is new, the soil is clay and repels water.
I’ve added sand, manure, potting soil, and straw...fertilizer....
Was it the heirloom seeds?
Was it the heat?
Was it the soil that needs to be worked more?
I know for sure that because of the heat every plant, shrub, and tree I planted has been in survival mode.
Now the weather is cooling, and we got a good rain last night!