Regarding question number 1:
I believe this is allowed. From my understanding Tuck's EA is non-binding while Columbia's is. Therefore you can apply to both, however if you get into CBS ED, you need to withdraw from Tuck.
Regarding question number 2:
I don't think 8 schools is too many. I personally applied to 6 and thought about doing more. It all depends on the amount of effort you want to put in (it does take a decent amount of time crafting an entire cohesive application) and money you want to spend (application fees can start to add up). You also need to consider your recommenders, who will likely have to write at least one for each school, but if you give them a heads-up when you ask they can give you a good idea whether or not they're up for the work.
It seems like you have a decent plan, I'm assuming that you won't apply to the schools in the later rounds if you get into at least one in the earlier rounds? I applied to all of my schools in the earliest rounds possible because I knew for all of them, if I got in I would go and as a borderline applicant for all of them, I figured the earliest rounds would give me the best chance of an admit. Another advantage of applying earlier is that they also haven't given out any scholarship money yet (if you know you are a competitive applicant, chances of obtaining a scholarship are likely higher in the earlier rounds).
Anyways, you seem to have a sound strategy.

with the school visits and the apps!