I don't understand too much about rakugo and Natsumi looks to be a nice person, she sent a simillar bouquet to Tanaka's wife for her first show with her band, nelca. I think that Natsumi and Hosei follow each other at Twitter
Yeah they do follow each other and ah that was so nice of her.
Oh no worries, I only know from following Housei's work. It's basically like a solo stand-up comedian except they sit / kneel down. They either tell traditional comedy stories (like Jackanory) and play all the parts in the story. Or they tell funny stories from their own experiences or just general observations, like you would expect from a stand-up comedian in the West. They're restricted to sitting and only using a fan or a towel as props to tell their stories. They spend years training under a teacher and then slowly climb the ranks.
There's actually a few English rakugo. Here's a British born one explaining each aspect of rakugo: