Summersoff, I believe the plant you have in the first photo is Chamaedorea elegans, also known as Parlor Palm. As to if it will grow into a larger palm from it's current size, I cannot say (I do not know that much about this particular plant, but at least a name will help you if you want to research it online). As to the second photo, I saw one of these just the other day, I don't remember what it stated the species was, but it is a species of Dracaena, I think it might be Dracaena sanderiana, which is also known as Lucky Bamboo. Lucky Bamboo as you mentioned, is also a species of Dracaena, not bamboo as some people think. It looks to me that the stems present on this plant are stems of the plant itself, but its top growth (leaves) has been stunted (by growing the plant so its stems become a certain thickness and then chopping off the top section of growth, causing new "shoots" to form at the tops, creating the foliage you see). To me, it looks like a really thick version of Lucky Bamboo, which makes me think it might be Dracaena sanderiana. It is similar to your Corn Plant, which is also a species of Dracaena (usually Dracaena fragrans). However, your Corn plant is not growing on its original stem (see below). Just some information on your Corn plant in case you didn't know but were interested: It is a piece of cane rooted in the soil (the foliage on top of the corn plant is the Dracaena fragrans) with some Dracaena "grafted" or "air layered"-- I don't know exactly how they do it-- into the cane which creates what you see and know as a Corn Plant. I hope this information has been helpful. Planto

Man, I love this site. I get answers to questions I didn't even know I had! I have one of those in an area I haven't tamed yet. Thanks for identifying it, now I won't pull it out. Thanks!

Now I'm puzzled as to why you asked for an id (using a photo dated 2015) if you already knew its name and had posted about it before? Your plant hasn't got typical Ixora foliage which is why I didn't recognise it. I'm thinking it could be Ixora 'Siam Ribbon' which has curled and distorted foliage. Reading up on its requirements I doubt it will flower in a terrarium as it likes full sun. Siam Ribbon

Looks like a California poppy seedling to me, Eschscholtzia californica.