IME, most hospitals aren't going to assign you much in the way of procedures, nursing student or not, unless you are in a specialized unit (like ICU, CVICU, CCU, etc.) and it seems that you already do most of them: EKGs, blood draws, removing peripheral IVs and discontinuing foley catheters.
Where I work, the hospital hires nursing students as techs after completion of Nursing I, but this doesn't make them any different from any other non-student tech or CNA. They still mostly help patients with ADLs, do baths, vital signs and accuchecks, and stock supplies/linen. If interested, they may be taught how to remove IVs and catheters and checked off to do so independently, but ours do not do EKGs or draw blood, (we have EKG techs and a phlebotomy team.)
Just wondering - where do you see this going? If I may, as a former tech myself before becoming a nurse, I would be careful about expanding your duties before becoming licensed. You may end up bearing liability that you have no business worrying about when working outside of an assistant capacity. While some hospitals will look the other way and allow you to do more than you should be, know that others may throw you under the bus should anything untoward happen. You will not have a leg to stand on, nursing student or not. Protect yourself first; you will practice lots of nursey skills in clinical and should limit your activities when outside of school to your job description. As one instructor told me, "the only time it matters that you're a student nurse is while you're at school."
If you'd like to do more, apply to nurse extern positions while you're in school. Observe everything you can. Offer to float to other floors for more experience. Go to all the education provided to you. Just don't stick your neck out when you're not licensed yet!
If I were you, I would contact the Department of Health and Senior Services to find out the scope of practice for PCTs/CNAs in NJ first. They should be able to give you some direction, within broad terms, where you can expect to go with this. Good luck!