Begonia

'Marksbegonias' is the site expert on begonias, so in case he doesn't see the question, send him a private message!

Looks a beautiful bloom. I'm certainly no expert, but i do grow Begonias and will do my best to help.
I have just written a blog "Double Tuberous Begonias, What's happening next" hope that helps. You may find the house too dry an atmosphere, although if they're going down i wouldn't think it as important as when they're growing.
The huge flower, as you say, is the male flower. There are generally 2 female flowers behind this which you should take out to get the best from your showy male bloom.
Is this a named variety? not all double tuberous Begonias are named - they have to be grown on trial for a period (i think 5 years) before they become a named exhibition Begonia, before that they have a number. Some unnamed ones can be just as nice, but when showing i go for the named ones which i get from Begonia specialist nurseries which for some new ones can be up to £30. If it is a named one, it looks a bit like "Tahiti" but i'm not sure.
I have seen some cheap named Begonias in garden centres and have tried them, but they haven't got the same quality as the ones from the specialists.