I better start my comment off by saying that I'm... uh... not really into the whole manga style much. But you said you'd like suggestions and comments, so here we go.
(Hope I'm not moving too much into TT&T territory here.)
That said, the art is really cute, even if it's not my cup of tea personally. Inking, colouring and the speech bubbles are nice and clean, that's more than I can say about the majority of webcomics out there. Some pages / panels are a bit confusing so I had no idea what was going on at first glance... Like the near-car accident scene. Drawing "action" scenes isn't easy. And it didn't happen a lot otherwise, though.
The comic follows the ways of manga not only in the art style, but also in the writing / story. So while this may appeal to manga-fans, I found it unfortunately kinda predictable. (There are just sooo many manga-ish comics that start out with the main character oversleeping and barely making it to school in time!) o_o
However, the story has only just started, and what you mentioned about the future of the story sounds much more interesting than what we've seen so far... so, guess we'll just have to give the story a bit more time.
Anyway, I think there is definitely potential. The main problem I see really is that you only update monthly now. It's just really hard to follow a story and get to know the characters (which is essential if you want the readers to really care about the comic) with that few updates.

And even with so few updates, there are a lot of fillers. I'd recommend you to move past fillers into an extras / art section as they are annoying for some people who read through the archive.
Hope I didn't come off as destructive. I criticise because I care!
(Oh, and kinda off-topic: Your gen-chan's cute.)