Excelent credentials. You certianly have a shot at honors in CSE, but it sounds like that isnt the field of study you are interested in.
Generally speaking, your intended major drives your choice of college. There are a few majors, like comp sci, that are offered in more than one (CSE, CLA). If you want to major in biology you wont get that degree from CSE.
CSE is a tougher admint right now, but I wouldnt say that means its more prestigous. Just tougher.
Yes, you are more likely to get into honors in CBS, and possibly better scholarship chances, but most are U wide. Again, though, its pointless if you dont want a CSE degree.
Not sure what to say about the app, other than try to fit it into the space they have. GL.