She asks him out at the pool and she came from nowhere. Seemingly liking him for a long time! How and why did she chose to date him? We didn’t see anything regarding how and why she picked him to date for 6 months. I’ve never read the manga, is there any explanation? 

As long as remember, Iroha went to pool because she also got detention although i don't remember what her mistake. Meanwhile tsun tsun go to the pool because he got threatened. He force himself to clean the pool because he doesn't want to be known as irresiponsible person. He thought Iroha will not come because of the rumor surround her. So he little taken aback when Iroha finally come. When Iroha teasing him he blurt out his thought based on the rumor that he heard. He feel bad about that and his friends advice him  to apologize. He did not know how so he follow her all day long and end up watching her on the bookstore. When Iroha get accidentally accused as shoplifter, Tsun tsun came to the rescue by confessing that he is stalking her all day long so he is really sure that Iroha is innocent. After that, iroha became really interested on tsun and decide to asking him out  in the class. 

If anyone is unclear on how they initially meet and why, the movie is based on the anime of the same name. It's (as of 2020) two seasons long with 12 episodes each (24 episodes total) and it explains a whole lot that the movie probably (I haven't watched it yet) does not go over. I would highly recommend checking out the anime or reading the manga (the manga probably goes into more detail as it usually should).