Your post appeared in two places, and maybe you didn't see this reply I made elsewhere.
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Pepino "melons", Solanum muricatum (so actually a member of the tomato/potato/chilli family) that I have bought in shops in Chile are about 6-8"/15-20cm long, and oval in end-to-end cross-section. So a bit bigger than an aubergine, but rather smaller than most melons. But there is a picture of one on the Wikipedia page, described as ripe, not much larger than a hen's egg, so they can be rather smaller than that. They do look like melons.

Their origin is, like many of the cultivated solanums, in the Andes. The original wild plant has not been found. They are cultivated at around 2000m to 3000m in the tropical Andes, and in the mediterranean climate area of Chile. I came across them being grown at around 1500m in the Cameron Highlands of Malaysia, but they weren't very good, perhaps too warm. I believe they are also grown in the northern parts of New Zealand.

They are known to be trickier than chillis to grow. But in general, I would say that if you have the conditions right to grow aubergines without any trouble, or tamarillos (tree tomatoes), then you should have the conditions about right for these.
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Additional comments on your latest:

Solanums are generally self-pollinating.

Solanum flowers are generally pretty obviously different from curcurbit (squash family) flowers, though if you are total newbie you may not recognise the difference. A few images from google might help. If you decide what you have is a curcurbit, then it wasn't a pepino melon, you were misled. But this is always a problem when plant sellers sell things with just popular names.