Looks like an Epiphyllum type. I would just leave it. Don't know why it hasn't flowered. Probably as you say wrong food. I would leave it to starve now, but I'm not a cactus expert. Hywel would know.

I thought Epiphyllum too but if so its not how it should be. I suspect its had too much water and too much fertilizer.
How much light does it get?
If that's what it is, and I've never seen one with that lax habit ,I'd repot it into a slightly larger pot and stop being so kind to it. It needs a very open compost with a lot off humus and some sand, so not your average cactus compost. It needs to be kept pretty dry over the cooler months and even in summer once a week is plenty. If you really want to fertilize it stick to one watering with tomato fertilizer in late spring, but not until its got strong upright growth.

If Hywel sees the question and can give you a better identification the treatment will most likely be the same. You can't "prune" it as such though you can cut off stems and root them in very sandy dry compost.

Thanks a lot