TAP, NYS aid and PELL (federal aid) are entitlements. If you are eligible for them, you will receive them.
City Tech has both 2 year and 4 year programs. Unless you specifically applied for a two year program that is not competitive, I would not assume that you have already been accepted. There are programs; hospitality management, Culinary Arts, Fashion, Computer Science, School of Technology that fill up fast leaving very few seats for spring admits
Illustration/ Game Design Graphic is the 4-year degree program
http://www.citytech.cuny.edu/communication-design/communication-design-btech.aspx.
No, that is not how it works. You do not get aid if you are not in school.
If you are in school for only one semester
your tuition is $3165 for the semester
http://www.citytech.cuny.edu/admissions/tuition-general.aspx
you will only get half of the TAP award, which is ~ $1500
What is your EFC? You are not getting full TAP (which is ~ $5165 for a 0 EFC)
You will get ~ 5000 in Pell for the year if your EFC is ~ $700
http://www.ega.edu/images/uploads/2016-2017PellPaymentSchedule_Portrait.pdf
Since you will only be in school for the spring semester, you will only get half of the Pell (provided you are enrolled full time). If you are entitled to $5000 in Pell, you will only receive $2500.
Based on what you wrote, you will receive approx $4k in federal and state aid. After the deduction of tuition, you will be left with $835 (less after they deduct fees).
No matter how much your cost increase, you will not get increased TAP or PELL.