A lot of this is speculation, of course. All that is publicly known in English is what I've translated and some spoiler information left behind on MangaFox by a guy who skimmed through the story in Japanese.
So, I will indulge in a little bit of educated speculation of my own:
Spoiler:
(1) I am guessing that Banri got knocked off the bridge by accident by somebody who bumped into him while jogging or bicycle riding. He didn't notice them coming because he had his ear-buds in and the volume turned up.
(2) Linda tended to consider Banri as a sort of little brother she needed to protect. That is why she wouldn't accept his confession right away. Now, however, Banri is considerably more mature, and she finds herself attracted to him. Contrary to some other opinions I've heard, I cannot believe that Linda doesn't know anything about his accident. Shizuoka isn't Tokyo, Tokyo is a big place, and finding her in the same college as Banri is simply too much of a coincidence. Either she asked his parents to make sure that he went there, or she transferred there once she discovered to which school he had been accepted.
(3) There are aspects of Banri that are remembered at a subconscious level. His memory loss was quite selective: he forgot his parents and friends, but not society and Japan in general. The subconscious memories are why, in my opinion, he reacted so strongly to Kouko's request for him to wait. Linda's request for him to wait still hurt at a subconscious level.
(4) Banri will recover his memories at some point. That is a given. I understand that this will happen temporarily in volume 4. Apart from that, though, there will have to be a reconciliation between the old and new Banris before the story can end.