Yes you are correct. My wife is going to be heartbroken about this :(
The plant shop where she bought this a long time ago told her it was Bleeding Hearts. But the dead giveaway are the leaves which are that of Begonias.
Yes that is a bougainvillea at the background. Here's a closer look.
Begonias are also very pretty plants and can grow quite big!
That is lovely! I see them growing around here, but I dont have space to have one.