Potatoes

Certainly you could remove the flowers as an aid to i ncreasing the yield. It saves the plant putting its energy into seed production so it concentrates on making tubers. However, the leaves are the bits which produce the food which feed the tubers, so remove them and you reduce your crop.
You can remove the foliage once it begins to die down as it then is no longer of use to the plant.
You may, should in fact, remove the foliage if you have blight. This definitely reduces the crop, but it does mean that you at least get one which is clean.

i believe you can leave the potatoes in the ground well after the plants have died as they wont shoot till next spring

Unless we get blight I don't remove the tops of the potatoes until they have died off completely.