What are my chances of getting into University of Minnesota - Twin Cities CSE?

Here are my stats:

Unweighted GPA:
3.9348
Weighted GPA:
4.6304

Class Rank:
28 out of 716 (~top 4%)

New SAT:
English - 730
Math - 750
Total - 1480

Extracurricular Activities:
Varsity Tennis, National Honor Society, Science National Honor Society, and Key Club.

Course Rigor:
I will finish senior year of high school having taken 12 AP courses.

Race:
Asian

Gender:
Male

Choice of Major:
Chemical Engineering

Can I get into the College of Science and Engineering and get my choice of major? Also, is it possible for me to get some aid (I am an out-of-state student and the cost of attendance is just a little above our budget)?

Here are the latest stats for the class entering this fall - you can see that your stats line up well:

https://admissions.tc.umn.edu/academics/profile.html

You are admitted to a college, not to a major. Some majors in CSE are going to be harder than others to qualify for but all of them likely require you to satisfy a certain technical GPA and course-load. You can read about those here:

https://www.advising.cse.umn.edu

https://www.advising.cse.umn.edu/cgi-bin/courses/noauth/ud-requirements

https://www.advising.cse.umn.edu/cgi-bin/courses//noauth/tgpa-courses

You would know your financial situation best - UMN isn’t going to have a lot of institutional funds for need-based aid. However, they do make some merit aid available to out of state students, particularly the National:

https://admissions.tc.umn.edu/costsaid/schol_campus.html

Good luck to you!

Assuming you are admitted which appears very likely, you may be offered a scholarship that covers the OOS portion of tuition, because you are in the top 10% of your class. If you are a National Merit Finalist, you could be offered the biggest OOS scholarship that pays another $10,000 toward tuition, because that has a preference for NMF. The university also has lots of smaller scholarships, and the various colleges and majors also have scholarships, so it is possible that you could be offered multiple scholarships if you are very competitive among other applicants.

Your challenge is that you are applying to the most competitive college at the university. Plan on applying for financial aid, and consider working part-time if needed. Lots of students at the University of Minnesota hold part-time jobs, often in labs on campus doing things related to their major.