UH, I figured ill share the little bit of information i know in case you still have some grey areas of concern.
1. I guess your question is relatively the same in the sense that if your getting into a nursing school you are in the program. For example, you would be going to LIU you would be enrolled in the nursing program but at City Tech you are enrolled in City Tech and not so much their program.
2. Considering your pre-requisites are done, finishing a nursing program should be about 4 semesters considering nothing is failed or repeated.
3. I would say that you can take all of your pre-reqs at city tech just make sure that you are taking all of the reccomended courses for LIU so there is no discrepancy there.
pen up the link that states the pre-professional phase of nursing.
5. There is an extrance exam called the Hesi and it must be taking within 2 semester of starting the program and passed with a grade of 75% in the required sections.
6. If i were you with the amount of drive that you seem to have i would persue the BSN and i understand how you feel about the pressure from family members but one thing i have learned is not to compare yourself to others. Everyones journey and path in life is different. Just keep your mind on the prize and you will be fine.
Hope this helped.