How do I know if I am fit to do a PhD in my area of interest, specifically, theoretical CS, when my background was mostly applied EE?
Until you try, you wouldn't know if you can or cannot do it. There are plenty of people who make more radical switch of fields and make meaningful contributions. If you are very good at applied signal processing, you probably can get good at applied discret math and theoretical CS. One way to ease into the field is to take relevant grad-level courses. Try taking a theoretical CS class and put your best efforts to excel.

(I switched from CS to EE. I was very much into logic and computation theory before starting my PhD in adaptive signal processing.)