Chamaedorea elegans is correct. Those are definitely not Arecas.

Purple, we don't know where the OP lives but judging by the fact that the Sweet William is in flower presumably the pictures were taken a little while back. In which case Muscari armeniacum would be in leaf. In some climates, including mine it is evergreen anyway. M armeniacum is by far the commonest and weediest of the Muscari and going by the overgrown look of the beds I doubt anything choice is likely to have survived there. Since all the white part of the foliage in the photo would have been under the ground the foliage doesn't look particularly long to me. As you say Allium would be easy to id by smell. But I'm still putting my money on the grape hyacinth.

Sand is not a good soil component either unless only used in small amounts. I use unglazed, un-dyed coarse gravel from the pet store. Here it costs $2.99 for a 5-lb bag. I mix that about 50-50 with soil from my garden. The soil is high in clay. When wet, it stays together. When mixed with gravel, it crumbles apart easily. I also add lava rock for those species that are more sensitive to overwatering. For me, Stapeliads do not qualify. If I were exposing them to unobstructed rain, then I would add lots more drainage material. Most of my plants are protected from rain in an unheated greenhouse. Since I use garden soil, extra fertilizer is not necessary, and when I repot in 2-3 yrs, the new soil will have new nutrients. Keep in mind though the soil I use has minimal compost and humus. It would be considered poor. I have a patch where I "quarry" from that remains bare. I would repot now. Keeping them in peat increases the likelihood the roots will dessicate, making it also more likely for the plant to rot when you start to water in the spring. I water mine lightly occasionally during the winter. As far as temps go, I have never had a problem exposing my Stapeliads to temps down to 29-30F. They are still outdoors now. Even Pseudolithos from "hot" Somalia doesn't mind the cold. I'd bring them in but space is limited so I stretch it out as much as I can. x

My best guess would have to be a Bird of Paradise. Most likely a white Bird of Paradise. I had a white one before, and it resembled your plant.