I believe "~지 않다" and "~질 않다" are the same. I also believe that they both are present tense. #1. 집에서 나오지 않아. #2. 집에서 나오지를 않아. according to a Korean dictionary "를" is emphasizing word here. #3. 집에서 나오질 않아. This is way you speak #2 So "감이 오질 않아" is you are emphasizing you really don't know if he/she has the same feeling that you have for her/him. Please note that "나와 같을까?" can be translated many different ways depending on situations/circumstances.

감이 오질(<오지를) 않아 means the same as 감이 오지 않아. 를 can be sometimes used as delimiter(or focus marker 보조사). It just emphasizes the following word 않아.