One thing for you to think about: MIT and Caltech are very intense. Studying at MIT has been compared to drinking water from a fire hose, and Caltech is not much different. To attend either school you need to put an enormous amount of effort into your classes and your homework, and possibly some more effort into research opportunities. This is not going to leave much time for anything else. Do you want to do this?
At Stanford I still remember doing homework on many Saturday afternoons. Again, do you want to do this? Suppose you spend six hours on a sunny Saturday afternoon solving one problem on a homework assignment, for one class out of the five classes that you are taking. Do you feel great that you solved the problem, or do you feel like you just wasted a Saturday? Do you want to keep this up for a full 4 years?
I also think that Georgia Tech is a reach.
I also think of cancer as an enemy. There are a lot of us walking around after some degree of cancer treatment. A lot of smart people like you, except older, have helped to improve our treatment options quite a bit. Best wishes with this.
It is. This makes it tough to guess your chances at your reaches. Make sure that you apply to solid safeties.
To me your interests make me think that some form of graduate school is entirely possible. You can get accepted to very good graduate programs coming from your in-state public schools.
Best wishes. To me it sounds like you are on a good track.
And best wishes to your father.