This is a Beefsteak begonia, Begonia erythrophylla. It's kind of a nice old cultivar. It blooms for me every early spring. It is a rhizomatous begonia, so it will tend to sprawl over time. This is its natural growth pattern, so you want to place it in a wide pot as it grows. You can take cuttings of it pretty easily if it gets too rangy.

Yes, it appears to be a fern. Perhaps some type of Pteris.

Thank you. Just looked it up online and yes it fits the description perfectly

What a great question. I brought in a frond of the Japanese Painted fern and it died rapidly too. But then I don't know if there is a special way to cut ferns for floral arrangements. Should you take off the foliage that will be below the water like you would with rose leaves?