pomegranate and cactus

Today we started to talk about plants and what can and can't grow round here with Rosa. I was mostly interested in whether it's worth buying and trying to grow a small orange tree (there are some in our local garden center/shed). I am still not sure about the orange tree, but Rosa is also very interested in things that grow, so she shown us a some of her current favourites around the site - small pomegranate tree (even given us one tiny fruit of it) and a beautiful cactus blooms that will last just today. Don't know what cactus that is - maybe there are some experts reading, identification will be appreciated. The flower is about 12 cm in diameter, very pale magenta/pink, the bloom is taller than the rest of the plant

Cactus pictures to follow