I would pick Rutgers, UGA and Kansas (the latter two for the immersion in US Big College experience and great college town atmosphere. Rutgers for the department superiority (at least the grad dept) and access to NYC. I am not familiar with study abroad applications but I would tailor it just a little if that is possible. Are you saying each college would see what you wrote about the other? That would indicate a more general statement is more appropriate. Yes you would have a good opportunity to scope out Rutgers for possible grad studies and visit the other nearby prominent departments in NJ and NY as well.
It is only one personal statement that will be sent to each of the universities.
Can you select modules from another department like languages if your doing a Philosophy degree in the U.S.? I’ve read a lot that seems to suggest you can and you have a broader selection of modules. This is something I’d like to mention in my personal statement.
Yes, you can select classes (modules, in US speak) from any department you wish.