I planted my garden sweet corn next to a corn field next door and now my sweet corn isn't so sweet, what is happening? Unlike other vegetables that get cross pollinated and still taste as they should, sweet corn is the exception. When an apple or cucumber gets cross pollinated (and they have to be to get fruit), it is the seeds inside that get changed, not the fruit we are eating. Those characteristics come from the female flower. With sweet corn then we are eating the seeds. The sweetness is diluted by the DNA from the field corn. It may look like it is supposed to, just not taste like it should. Next year plant the sweet corn as far as possible from the field corn.
I saved my cucumber seed from 2015, but this year my cucumbers are not cucumbers at all. The cucumbers you grew in 2015 were likely a hybrid with specific DNA to give you that high yielding, disease resistant variety. Cucumber plants are pollinated by insects that very likely were visiting other kinds of vine crops at the time. Your female cucumber flower received pollen from a summer or winter squash, perhaps a pumpkin. The seeds inside your cucumber from 2015 are not going to produce more cucumbers in 2016. What you are getting are some characteristics from both parents.
I let a volunteer tomato/ cucumber/pumpkin/gourd grow from the side of my compost pile to see what I would get and I did not get too much, just a lot of foliage so far, should I leave it longer? Any volunteer garden plant that was once a hybrid will be a very poor next generation plant. The characteristics that made it so good last year are now gone and it has reverted. Unless you have the room and time to wait, a better use for the volunteer plant is to add it back to the compost pile.
My potatoes are flowering and have tomato fruits. How is that possible? Potatoes and tomatoes are in the same family. We have bred the potatoes to have storage tubers underground and the tomatoes to have fruits above ground. If by chance a potato flower gets pollinated by wind, the result is a small fruit that resembles a tomato.
Hopefully you can see the common thread in the first three gardening questions. It is all about male and female flowers and the crossing of those male and female traits to give us the next generation of plants. When crossed by the breeders and growers, we get good things. When left to chance, the results are entirely different. Tomatoes and potatoes are wind pollinated, so it was chance that the potato flowers were pollinated. Now I wonder if we planted those seeds, what would we get??