Severe Common App supplement typo

For one of my college essays, I was writing about why Penn was right for me as at transfer, but the second time I named a school, I named Cornell–I had sent variants of this essay to a number of schools, and I’d forgotten to correct the second instance the school was supposed to be named. Am I an auto-reject applicant?
Throughout the rest of the essay, I believe that it was clear that I was applying specifically for Penn–I planned out my entire academic career with course names/etc, named specific professors with their research and etc., and discussed my previous attempts at outreach for Penn’s on campus extracurricular activities. I’m hoping that the extreme specificity may make up for the error, but I’m not sure if that’s enough.
I emailed the adcoms, hoping that they would swap the supplement with a corrected version, but if they keep this former version, am I screwed?

Also, there was another typo, though more minor in nature, in a later portion of an essay. It went something like “I’ve always been interested in governance, refusing to give it up I’ve strived to excel in organic chemistry”. It’s supposed to be “…refusing to give it up AS I’ve strived to excel”.
I went through the rest of the essay and I found nothing. Both errors occur in the first two paragraphs.
So will those two typos break my application supplement?

In all honesty I’d say the first one is pretty bad :(. I kid you not, at every single info session I had at ivy league schools they did not fail to say: DO NOT write school X’s name on school Y’s essay - it makes it look like you aren’t serious and didn’t take the time to review your work carefully.

The other error is minor, I wouldn’t worry about it. On my common app essay I used em dashes, and it caused a technical glitch where the final word on two of my lines became split into two like this:
hell
o

I was freaking out (even though it technically wasn’t my fault), and have been accepted to some great schools despite this. Minor errors won’t make any difference, who knows if the reader will even notice. However something like accidentally writing another school’s name is unfortunately hardly unnoticeable :/.

Good that you contacted them with a corrected version, hopefully they’ll be understanding and accept it! Best of luck!!!