Will Ivy League schools tolerate low GPA?

Before I moved here, I had the idea of applying to around 20 colleges and pick from the ones I would get accepted. Then, I learned how wrong I was, but I still wanted to get into a prestige college. Well… that’s why I had 4 Ivy schools.

This is a piece of how I explained the grading system in my country (under the additional information section):
In the end of the senior year, there is a big test that must be taken to go to college. Colleges accept students according only to that test score, and high school grades serve only as extra points for the test score. Thus, my high school was highly challenging. All classes from all branches were mandatory to take each year, and all module tests were in one week. The reason is that school grades were not a key factor for the graduation score, and making the module tests slightly rushed would get students to study a lot and prepare them for the big test as well. However, this resulted with average tests scores of 70-80 in my school. That is why my scores were a little lower in Turkey.

Yes, I am a NYS resident. I submitted my fafsa, CSS, TAP, and noncustodial waiver forms.

My US only GPA is 4.14.

I didn’t quite understand what you meant by “Do you love the core.” My high school core or the college I will apply to?

I did not see the last two replies when I was deciding which colleges two apply. Right now, it is 9. It used to be 8 because my adviser told me that having more than that would make me look unconfident with getting into the reaches. Here is my list:
Harvard
Yale
Cornell
Carnegie Mellon
NYU
Boston College
U of Rochester (I live in Rochester, and I already applied to this one)
SUNY Binghamton
SUNY Stony Brook

I wanted to try Columbia or UPenn, but after reading the first guy’s reply, I went with Carnegie Mellon and NYU.

I am interested in getting into the medical field. My major will be biochemistry.

I am not really sure about the budget. I only have my dad as my parent, and he earns around $20,000 a year. He takes care of my sister too.