Thanks for all the help and suggestions. Their leaves and stem look more succulent than those of Lily of the Valley. I don't use mulch in this area but compost instead. And I noticed yesterday that the same kind of plant also grows near my compost pile which is in a shady area so it looks like they can grow in both sunny and shady areas. Another thing is they all bunch up together. Maybe I will just let them grow for a while and see if they will reveal themselves. Or I can post a more up-to-date photo later on. Please let me know if you think of other possibilities. Thanks again everyone.

Papaver somniferum - one of the Laciniatum group. Not a perennial. This post was edited by floral_uk on Fri, Jul 25, 14 at 4:56

Thank you very much for the ID's. The first one is near the spot where I saw the bad-looking P. mugo subsp. rotunda about which I asked an ID too. At first I though they were both the same species because they looked similar, but when I went too look closer then I could see the cones were definitely different. Funny part is that someone else suggested in that thread where I asked for an ID that it could be P. thunbergii. So I guess both trees are similar looking indeed. The second one I think comes from a hedge close-by that was (I think) never trimmed and therefore started producing cones. The third one is almost a miracle to me. Closest Abies koreana that I'm aware of is at least a few hundred meters away from where I found it. I'm very glad I dug it out too because A. koreana was also on my wanted list. :)

The pink variety could be the hybrid Primula × bulleesiana since they come in several colors. Maybe the pink one you saw?